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Urakawa Hajime  浦川 肇

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URAKAWA Hajime  浦川 肇

浦川 肇

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Researcher Number 50022679
External Links
Affiliation (Current) 2022: 東北大学, 情報科学研究科, 名誉教授
Affiliation (based on the past Project Information) *help 2018 – 2021: 東北大学, 情報科学研究科, 名誉教授
2016 – 2017: 東北大学, 高度教養教育・学生支援機構, 名誉教授
2015: 東北大学, 国際教育院, 名誉教授
2014: 東北大学, 高度教養教育・学生支援機構, 名誉教授
2009 – 2013: 東北大学, 国際教育院, 教授 … More
2007 – 2009: 東北大学, 大学院・情報科学研究科, 教授
2007 – 2009: 東北大学, 情報科学研究科, 教授
2008: 東北大学, 大学院情報科学研究科, 教授
2006: Tohoku University, Graduate School of Information Sciences, Professor, 大学院情報科学研究科, 教授
1993 – 2005: 東北大学, 大学院・情報科学研究科, 教授
1999: 東北大学, 大学院・情報科学, 教授
1998: 東北大学, 大学院情報科学研究科, 教授
1992: 東北大学, 教養部, 教授
1990 – 1991: 東北大学, 教養部, 助教授
1987 – 1988: 東北大学, 教養部, 助教授 Less
Review Section/Research Field
Principal Investigator
Geometry / Global analysis / Global analysis / 代数学・幾何学 / Mathematical analysis / Basic Section 12020:Mathematical analysis-related
Except Principal Investigator
代数学・幾何学 / Geometry / 解析学 / Global analysis … More / Basic analysis / Basic analysis / Geometry / General mathematics (including Probability theory/Statistical mathematics) / General mathematics (including Probability theory/Statistical mathematics) / Global analysis Less
Keywords
Principal Investigator
調和写像 / 熱核 / ヤング・ミルズ接続 / 無限グラフ / グリーン核 / スペクトル / Dirichlet eigenvalue problem / 本質的スペクトル / 強擬凸多様体 / 指数的ヤング・ミルズ接続 … More / 離散ラプラス作用素 / ディリクレ境界値問題 / 第1固有値 / ネットワーク / 離散曲面 / 有限要素法 / 2-調和写像 / 2-ヤング・ミルズ場 / 非正曲率 / コンパクト・リー群 / エネルギー / サイバーグ・ウィッテン方程式 / 2-ヤング・ミルズ接続 / 2-調和写像 / 軌道 / リーマン多様体 / アファイン接続 / チーガー定数 / infinite graph / affine connection / Green kernel / ディリクレ固有値問題 / Yang-Mills connection / リッチ曲率 / シュレーディンガー作用素 / 極小超曲面 / モース指標 / カテノイド / ヘリコイド / 極小曲面 / 群同変 / ヤコビ作用素 / モ-ス指標 / 確率分布 / 重み付きノルム不等式 / Yang-Mills接続 / 指数的Yang-Mills接続 / 正則ディリクレ空間 / Seiberg-Witten方程式 / 擬4元数構造 / ラプラシアン / 4元数ケーラー対称空間 / 双対接続 / 対数的ソボレフ不等式 / スペクトル・ギャップ / 斉次等質樹木 / 断面曲率評価定理 / ファジィ・グラフ / 根付き樹木 / ファジィタワーグラフ / 評価関数 / 情報幾何学 / アファイン微分幾何 / 射影的に平坦 / ファジィグラフ / 最速ロボット / 剛性行列 / 質量行列 / ファジー・ドラム理論 / 三角形分割 / 数値計算 / 隣接行列 / 離散線識曲面 / 非固有アファイン球面 / ピック不変量 / アファイン空間 / アファイン・シェイプ作用素 / 2-エネルギー / 完備リーマン多様体 / コンパクト・対称空間 / ラグランジアン部分多様体 / 一般化B.Y. Chen予想 / 非正曲率多様体 / バブリング理論 / mエネルギー / 複素射影空間 / 一般化B.Y.Chen予想 / 平均曲率ベクトル場 / 除去可能特異点定理 / コンパクト性定理 / 平坦多様体 / レイ・シンガーのゼータ関数 / フルヴィッツのゼータ関数 / エネルギー汎関数 / 2-エネルギー汎関数 / 対称空間 / 2-調和部分多様体 / 葉層多様体 / コーシー・リーマン多様体 / G-主束 / ねじれ束 / ハーマン作用 / 多重調和写像 / ユークリッド空間 / 極小 / 埋め込み / 主曲率 / リー群 / 2-エネルギー / バブリング現象 / m-エネルギー / 強擬凸リーマン多様体 / チェン予想 / CR類比 / テンション場 / k-調和写像 / ディリクレ境界固有値問題 / 調和射影 / 境界付グラフ / 離散ラプラシアン / 離散調和射 / 次数 / 射影平坦 / ワイル構造 / ディリクレ問題 / バルタの定理 / ファーベル・クラーンの定理 / グラフ / first eigenvalue / spectrum / harmonic morphism / graph with boundary / 擬調和写像 / シンプレクティック多様体 / ヤング・ミズル接続 / ワイル接続 / モデュライ空間 / 鋭角三角形分割 / 境界値問題 / 固有値 / 離散計算幾何 / 非退化CR多様体 / 擬エネルギー汎関数 / 共役接続 / ヤングミルズ接続 / finite element method / oseudharmonic map / symplectic manifold / 収束比率 / 可視化 / ディリクレ境界値固有値問題 / ノイマン境界値固有値問題 / 数値計算プログラム / ヤング・ミルズ場 / 孤立現象 / 複素スピン構造 / ディラック作用素 / ケーラー多様体 / カラビ・ヤウ多様体 / ノイマン固有値問題 / コーシー・リーマン・リー群 / レビ平坦構造 / heat kernel / convergence rate / Ricci curvature / bi-Yang-Mills connection / biharmonic map / visualization / 極小部分多様体 / 二重調和写像 / リーマン・ベクトル束 / 沈め込み / 二重調和ベクトル場 / 捻れ積 / 正曲率空間 / 等質空間 / 単連結 / 調和射 / 部分群 / 超曲面 / ファイバー束 / 二重調和 / コンパクト / 第一固有値 / 射影 / 等長はめ込み / G-主束 / 群作用 / コンパクト対称三対 / ベクトル束 / 葉層構造 / 調和ベクトル場 / 二調和ベクトル場 / リーマン主束 / リーマン沈め込み / k-調和写像 … More
Except Principal Investigator
調和写像 / 平均曲率 / グラフ理論 / 自由確率論 / 作用素環 / ランダム行列 / 自由エントロピー / 大偏差原理 / 量子確率論 / 量子中心極限定理 / 強擬凸多様体 / ヤング・ミルズ接続 / リー群 / 代数的符号理論 / 自己双対符号 / 有限体 / 格子 / 対数ソボレフ不等式 / 輸送コスト不等式 / トーリック多様体 / CR多様体 / アインシュタイン計量 / リーマン多様体 / 極小曲面 / 安定性 / harmonic maps / reaction-diffusion system / operator algebras / free probability theory / free entropy / large deviation principle / 結晶格子 / グラフの調和写像 / Discrete Laplacian / リー変換群 / ホワイトノイズ理論 / 量子ホワイトノイズ / 量子分解 / 散逸量子系 / White noise theory / Quantum probability / Quantum white noise / Quantum decomposition / Quantum central limit theorem / Levy Laplacian / Heegaard splitting / Dehn surgery / 熱核 / nonlinear partial differential equations / optimal stochastic control / viscosity solutions / Hamilton-Jacobi-Bellman equation / mathematical finances / homogenizations / ergodic problem / numerical analysis / ラプラシアン / 大域解析学 / スペクトル幾何学 / 測地線論 / Hー変形可能曲面 / 余次元1葉層構造 / プラス作用素 / シュレ-ディンガ-作用素 / 平均曲率一定超曲面 / リース・ボッホナー平均 / リトルウッド・ペリーのg-関数 / 代数体 / モジュライ / モンジュ・アンペール方程式 / ウェイヴレット / 不変部分空間 / コロフキン作用素 / ヤング-ミルズ接続 / 強星型関数 / 射影微分幾何学 / 発展方程式 / 曲面の変換 / 射影曲率 / 非線形方程式 / 平均曲率流 / 応用数学 / 代数的組合せ論 / 符号理論 / 離散幾何 / 組合せデザイン理論 / 置換群論 / 組合せデザイン / 国際情報交換 / ブルガリア : オランダ / 自由エントロピー次元 / 自由情報量 / 量子フィッシャー情報量 / 無限分解可能 / 自由エントロピート次元 / 対数Sobolev不等式 / 関数論 / 特殊領域 / ラインハルト領域 / チューブ領域 / 複素幾何学 / トーラス作用 / 正則ベクトル場 / アインシュタイン・ケーラー計量 / 可解多様体 / シンプレクティック構造 / 接触構造 / 測度距離空間 / エネルギー形式 / 変分収束 / Gromov-Hausdorff収束 / ネットワーク / 有効抵抗 / 2-調和写像 / 2―調和写像 / p-エネルギー / P-エネルギー / ホワイトノイズ解析 / 無限次元解析 / 複雑ネットワーク / 直交多項式 / 確率解析 / フーリエ-ガウス変換 / フーリエ・ガウス変換 / 等長変形 / ラプラス作用素 / ヤング / ミルズ場 / ゲージ理論 / ヤコビ作用素 / 葉層 / ハーディークラス / スミルノフクラス / Heinzの不等式 / エルゴディスクな作用 / 可変既約表現 / 亜群 / Helson-Sarasonの予報型定理 / 調和写像のモジュライ空間 / 値分布論 / Vojta予想 / ネバリナ理論 / 箙多様体 / ケーラー・リューヴィル多様体 / ヘシアン多様体 / 平坦な共形構造 / フアノ多様体 / ヤンミルズ接続 / ALE空間 / 中心アファイン的変形 / モジュライ空間 / hyperkahler多様体 / ケージ理論 / 反自己双対空間 / Hessian多様体 / アファイン多様体 / リューヴイル多様体 / harmonic map / moduli space of harmonic maps / value distribution theory / Vojta conjecture / Nevanlinna theory / quiver varietie / Kahler-Liouville manifolds / Hessian manifolds / アインシュタイン / カルノー群 / グラフのラプラス作用素 / 反応拡散方程式系 / 複素クライン群 / 二木指標 / グリーン関数 / カルノ-群 / Einstein / Carnot groups / Laplace operators on graphs / toric varieties / complex Kleinian groups / Futaki character / Dirac作用素 / スピン構造 / 等スペクトル問題 / 球面空間形 / スペクトラルゼータ関数 / グラフのラプラシアン / Dirac operator / Spin structure / isospectral problem / spherical space forms / spectral zeta functions / Laplacian for graphs / 非可換確率論 / 非可換エントロピー / ノルム不等式 / エントロピー / アメナビリティ / 行列 / noncommutative probability theory / noncommutative entropy / random matrix / norm inequality / 離散的ラプラシアン / 中心極限定理 / ハーパー作用素 / アルバネーゼ写像 / 標準的実現 / 格子振動 / 離散幾何学 / グラフ / スペクトル幾何 / 固有値 / Crystal Lattice / Harper Operator / Central Limit Theorem / 非コンパクト群 / 固定点 / 4次元球面 / 2次特殊複素線形群 / 2次特殊復素線形群 / Lie transformation group / non-compact group / fixed point / four dimensional sphere / complex special linear group / スペクトルギャップ / ループ空間 / 対数リボレフ不等式 / ディソクレ形式 / ギッブス測度 / ハルナック不等式 / Logarithmic Soboles inequality / Spectral Gap / Loop Space / 代数的符号 / 距離正則グラフ / スピンモデル / 保型形式 / モジュラー形成 / ALGEBRAIC COMBINATORICS / SELF-DUAL CODE / DISTANCE-REGULAR GRAPH / FINITE FIELD / SPIN MODEL / MODULAR FORM / LATTICE / 複素スペクトル / レヴィラプラシアン / 伊藤公式 / Complex spectrum / Quantum dissipation / 離散ラプラシアン / 非斉次ヤング・ミルズ方程式 / アインシュタイン・ワイル幾何学 / 総実代数体 / ラムダ不変量 / デーン手術 / ヘゴール分解 / CR manifold / pseudoharmonic map / Yang-Mills theory / Einstein-Weyl geometry / Greenberg's conjecture / P-class number / 無限グラフ / スペクトル / グリーン核 / 岩澤不変量 / Z_P拡大 / Greenberg予想 / Harmonic morphism of graph / Inhomogeneous Yang-Mills equation / Einstein-Wey1 geometry / Totally real field / Lambda invariant / 二木不変量 / 複素フィンスラー多様体 / エネルギー汎関数 / 反応拡散系 / 活性因子・抑制因子型反応拡散系 / 概複素構造 / ヤン・ミルズ接続 / シンプレクティック多様体 / ケーラー多様体 / 解析的連接層 / 複素フィンスラー空間 / 回転面 / 概正則写像 / 完備双曲性 / 平均曲線 / 活性因子-抑制因子型の反応拡散系 / ディリクレ境界値固有値問題 / Futaki invariant / complex Finsler manifold / energy functional / mean curvature / heat kernel / crystal lattice / 粘性解理論 / 数理ファイナンス / ホモジェニゼイション / 多重スケールモデル / 非完備金融市場モデル / 最適制御理論 / エルゴード問題 / 偏微分方程式の数値解析 / 非線形退化楕円型方程式の解の平滑性 / 非線形熱方程式の解の安定性 / ショックの現れる非線形一階偏微分方程式の解の存在と一意性 / ハミルトンャコビベルマン方程式の数理ファイナンスへの応用 / 界面の発展方程式 / 変分法の数理生物学への応用 / 非線形偏微分方程式の数値解析 / 確率解析と非線形偏微分方程式の関わり / 作用素 / ユニタリ不変ノルム / 作用素単調関数 / operators / random matrices / transportation cost inequality / unitarily invariant norms / レヴィ・ラプラシアン / グラフのスペクトル / Dissipative quantum system / Spectral analysis of graphs / アーベル多様体 / 形式群 / ガロア表現 / ガウス写像 / ホモトピー類 / 多様体 / 曲率 / ヤングミルズ接続 / 等質空間 / リー接触構造 / リ-接触構造 / 複素多様体 / 力学系 / 熱方程式 / リッテ曲率 / リ-マン多様体 / 対称空間 / ラプラスベルトラミ作用素 / 部分多様体 / manifold / Einstein metric / curvature / Yang-Mills connection / homogeneous spaces / minimal surfaces / Lie contact structure / Laplacian Less
  • Research Projects

    (44 results)
  • Research Products

    (216 results)
  • Co-Researchers

    (110 People)
  •  Development of Theory of Harmonic MapsPrincipal Investigator

    • Principal Investigator
      Urakawa Hajime
    • Project Period (FY)
      2018 – 2021
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 12020:Mathematical analysis-related
    • Research Institution
      Tohoku University
  •  Development of Theory of Harmonic MapsPrincipal Investigator

    • Principal Investigator
      Urakawa Hajime
    • Project Period (FY)
      2013 – 2017
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Mathematical analysis
    • Research Institution
      Tohoku University
  •  New development of harmonic mapsPrincipal Investigator

    • Principal Investigator
      URAKAWA Hajime
    • Project Period (FY)
      2009 – 2012
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  Quantum Probability Theory and Infinite Dimensional Analysis

    • Principal Investigator
      OBATA Nobuaki
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      Tohoku University
  •  Convergence theory of metric measure spaces and its development

    • Principal Investigator
      KASUE Atsushi
    • Project Period (FY)
      2007 – 2009
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Research Field
      Geometry
    • Research Institution
      Kanazawa University
  •  Study of special domains and its application to complex geometry

    • Principal Investigator
      SHIMIZU Satoru
    • Project Period (FY)
      2006 – 2009
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Tohoku University
  •  可解多様体の諸構造の研究

    • Principal Investigator
      SAKANE Yusuke
    • Project Period (FY)
      2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Osaka University
  •  Applications of algebraic methods in coding theory to combinatorial designs and discrete geometry

    • Principal Investigator
      MUNEMASA Akihiro
    • Project Period (FY)
      2005 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Tohoku University
  •  Study of free probability and operator algebras based on random matrices

    • Principal Investigator
      HIAI Fumio
    • Project Period (FY)
      2005 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  Global analysis of the heat kernels on Riemannian manifolds and graphsPrincipal Investigator

    • Principal Investigator
      URAKAWA Hajime
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  Nonlinear theory of quantum white noise and its non-Gaussian extension

    • Principal Investigator
      OBATA Nobuaki
    • Project Period (FY)
      2003 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      Tohoku University
  •  Geometry of Harmonicity

    • Principal Investigator
      BANDO Shigetoshi
    • Project Period (FY)
      2002 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  Nonlinear elliptic and parabolic PDEs, theories and applications

    • Principal Investigator
      ARISAWA Mariko
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Tohoku University
  •  Study of noncommutative analysis and free probability theory on operator algebras

    • Principal Investigator
      HIAI Fumio
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  凸体の幾何とファジー力学系Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      2001 – 2003
    • Research Category
      Grant-in-Aid for Exploratory Research
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  Global Analysis of the heat kernel and Green kernel of an Infinite GraphPrincipal Investigator

    • Principal Investigator
      URAKAWA Hajime
    • Project Period (FY)
      2001 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  ALGEBRAIC CODING THEORY, COMBINATORIAL DESIGNS AND ASSOCIATION SCHEMES

    • Principal Investigator
      MUNEMASA Akihiro
    • Project Period (FY)
      2000 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      TOHOKU UNIVERSITY
      Kyushu University
  •  Quantum white noise and nonlinear infinite dimensional analysis

    • Principal Investigator
      OBATA Nobuaki
    • Project Period (FY)
      2000 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      Tohoku University
      Nagoya University
  •  GEOMETRY OF NUMBERS AND CODING THEORY

    • Principal Investigator
      UCHIDA Koji
    • Project Period (FY)
      2000 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Tohoku University
  •  射影不変平均曲率流と画像処理

    • Principal Investigator
      SASAKI Takeshi
    • Project Period (FY)
      1998 – 1999
    • Research Category
      Grant-in-Aid for Exploratory Research
    • Research Field
      Global analysis
    • Research Institution
      Kobe University
  •  Fundamental Research of Discrete Geometric Analysis and Its Applications

    • Principal Investigator
      SUNADA Toshikazu
    • Project Period (FY)
      1998 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (A).
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  Global Analysis of the Spectrum of an Infinite GraphPrincipal Investigator

    • Principal Investigator
      URAKAWA Hajime
    • Project Period (FY)
      1998 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (B).
    • Research Field
      Global analysis
    • Research Institution
      Tohoku University
  •  Lie transformation group of non-compact groups

    • Principal Investigator
      ASOH Toru
    • Project Period (FY)
      1998 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  Siochastic Analysis on loop spaces

    • Principal Investigator
      AIDA Shigeki
    • Project Period (FY)
      1998 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Osaka University
      Tohoku University
  •  凸体の配置の幾何とファジー数理Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Exploratory Research
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  Complex Manifolds and Gauge Theory

    • Principal Investigator
      BANDO Shigetoshi
    • Project Period (FY)
      1997 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      TOHOKU UNIVERSITY
  •  SPECTRAL GEOMETRY

    • Principal Investigator
      IKEDA Akira
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Study of noncommutative probability and noncommutative entropy

    • Principal Investigator
      HIAI Fumio
    • Project Period (FY)
      1997 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      TOHOKU UNIVERSITY
      Ibaraki University
  •  無限グラフと無限可積分系Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research on Priority Areas
    • Research Institution
      Tohoku University
  •  情報数理,グラフ理論そして微分幾何Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  調和関数に関連した関数空間の研究

    • Principal Investigator
      望月 望
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Tohoku University
  •  幾何学に現われる非線形方程式の総合的研究Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1995
    • Research Category
      Grant-in-Aid for Co-operative Research (A)
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  情報数理と微分幾何Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1995
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  調和写像とヤング・ミルズ接続の研究Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Tohoku University
  •  Geometric structures on manifolds and global variation problems

    • Principal Investigator
      SAKANE Yusuke
    • Project Period (FY)
      1994 – 1995
    • Research Category
      Grant-in-Aid for Co-operative Research (A)
    • Research Field
      Geometry
    • Research Institution
      Osaka University
  •  ヤング・ミルズ接続の量子化Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for Scientific Research on Priority Areas
    • Research Institution
      Tohoku University
  •  多変数フーリエ級数の球形和の挙動

    • Principal Investigator
      KANEKO Makoto
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Tohoku University
  •  幾何学的変分法と大域解析Principal Investigator

    • Principal Investigator
      浦川 肇
    • Project Period (FY)
      1992
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Tohoku University
  •  Hー変形可能曲面に関する剛性の研究

    • Principal Investigator
      KENMOTSU Katsuei
    • Project Period (FY)
      1991
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Tohoku University
  •  大域解析学とスペクトル幾何学

    • Principal Investigator
      北原 晴夫
    • Project Period (FY)
      1990
    • Research Category
      Grant-in-Aid for Co-operative Research (A)
    • Research Field
      代数学・幾何学
    • Research Institution
      Kanazawa University
  •  可微分多様体の研究

    • Principal Investigator
      高木 斉
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Tohoku University
  •  関数論の関数解析的研究

    • Principal Investigator
      大野 芳希
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Tohoku University
  •  可微分多様体の大域的構造について

    • Principal Investigator
      SHIOHAMA Katsuhiro
    • Project Period (FY)
      1988 – 1990
    • Research Category
      Grant-in-Aid for Co-operative Research (A)
    • Research Field
      代数学・幾何学
    • Research Institution
      Kyushu University
  •  代数多様体の整数論的研究

    • Principal Investigator
      中村 哲男
    • Project Period (FY)
      1987
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Tohoku University

All 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 Other

All Journal Article Presentation Book Patent

  • [Book] 代数学 第2巻2020

    • Author(s)
      藤原松三郎、浦川肇、高木泉、藤原毅夫
    • Total Pages
      693
    • Publisher
      内田老鶴圃
    • ISBN
      9784753601622
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Book] Geometry of Biharmonic Mappings--Differential Geometry of Variational Methods--2019

    • Author(s)
      Hajime Urakawa
    • Total Pages
      348
    • Publisher
      World Scientific Publishing, Co. Pte. Ltd.
    • ISBN
      9813236418
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Book] Geometry of biharmonic mappings, Differential geometry of variational methods2019

    • Author(s)
      Urakawa, Hajime
    • Total Pages
      348
    • Publisher
      World Scientific Publishing Co. Pte. Ltd.
    • ISBN
      9789813236394
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Book] Spectral Geometry of the Laplacian2017

    • Author(s)
      Hajime Urakawa
    • Total Pages
      310
    • Publisher
      World Scientific Publishing, Co. Pte. Ltd.
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] 数学解析第一編、微分積分学、第1巻2017

    • Author(s)
      浦川 肇、高木 泉、藤原毅夫
    • Total Pages
      636
    • Publisher
      内田老鶴圃
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] 微分積分学第2巻2017

    • Author(s)
      藤原松三郎、浦川肇、高木泉、藤原毅夫
    • Total Pages
      634
    • Publisher
      内田老鶴圃
    • ISBN
      9784753601646
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] Spectral Geometry of the Laplacian2017

    • Author(s)
      Hajime Urakawa
    • Total Pages
      309
    • Publisher
      World Scientific Publishing Co. Pte. Ltd., Singapore
    • ISBN
      9789813109087
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] 数学解析第一編、微分積分学、第2巻2017

    • Author(s)
      浦川 肇、高木 泉、藤原毅夫
    • Total Pages
      600
    • Publisher
      内田老鶴圃
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] Geometry of the Laplacian2016

    • Author(s)
      Hajime Urakawa
    • Total Pages
      370
    • Publisher
      World Sientific
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] スペクトル幾何2015

    • Author(s)
      浦川 肇
    • Total Pages
      338
    • Publisher
      共立出版(株)
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Book] ラプラシアンの幾何学と有限要素法2009

    • Author(s)
      浦川肇
    • Total Pages
      264
    • Publisher
      朝倉書店
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Book] ラプラシアンの幾何と有限要素法2009

    • Author(s)
      浦川肇
    • Total Pages
      272
    • Publisher
      朝倉書店
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Book] 微積分の基礎2006

    • Author(s)
      浦川肇
    • Total Pages
      230
    • Publisher
      朝倉書店
    • Data Source
      KAKENHI-PROJECT-18540154
  • [Book] Foundation of Calculus2006

    • Author(s)
      H.Urakawa
    • Total Pages
      232
    • Publisher
      Asakura Shoten
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Book] 微積分の基礎2006

    • Author(s)
      浦川 肇
    • Total Pages
      232
    • Publisher
      朝倉書店
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Book] 微積分の基礎2006

    • Author(s)
      浦川 肇
    • Total Pages
      230
    • Publisher
      朝倉書店
    • Data Source
      KAKENHI-PROJECT-18540154
  • [Book] 数理システム科学2005

    • Author(s)
      浦川肇ほか
    • Total Pages
      338
    • Publisher
      放送大学
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Harmonic maps and biharmonic maps for double liberations of compact Lie groups2022

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 51

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Harmonic morphisms of compact homogeneous spaces of positive curvature2021

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Note di Matematica

      Volume: 41

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic Hermitian vector bundles over compact Kaehler manifolds and compact Einstein Riemannian manifolds2020

    • Author(s)
      Urakawa, Hajime
    • Journal Title

      Note di Matematica

      Volume: 40 Pages: 1-16

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic homogeneous submanifolds in comopact symmetric spaces and compact Lie groups2019

    • Author(s)
      Ohno, Shinji, Sakai, Takashi and Urakawa, Hajime
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 49 Pages: 47-115

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups2019

    • Author(s)
      Shinji Ohno, Takashi Sakai and Hajime Urakawa
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 49

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic maps on principal G-bundles over complete Riemannian manifolds of nonpositive Ricci curvature2019

    • Author(s)
      Urakawa, Hajime
    • Journal Title

      Michigan Mathematical Journal

      Volume: 68 Pages: 47-115

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Harmonic maps and biharmonic Riemannian submersions2019

    • Author(s)
      Urakawa, Hajime
    • Journal Title

      Note di Mathematica

      Volume: 39 Pages: 1-23

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic maps on principal G-bundles over complete Riemannian manifolds of non-positive Ricci curvature2018

    • Author(s)
      H. Urakawa
    • Journal Title

      Michigan Mathematical Journal

      Volume: 67 Pages: 1-14

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Polyharmonic maps into the Euclidean space2018

    • Author(s)
      N. Nakauchi and H. Urakawa
    • Journal Title

      Note di Matematica

      Volume: 38 Pages: 1-12

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic submanifolds in a Riemannian manifold2018

    • Author(s)
      N. Koiso and H. Urakawa
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 55 Pages: 325-346

    • NAID

      120006478932

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Rigidity of transversally biharmonic maps between foliated Riemannian manifolds2018

    • Author(s)
      S. Ohno, T. Sakai and H. Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 47 Pages: 1-15

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Harmonic maps and biharmonic maps on principal bundles and warped products2018

    • Author(s)
      H. Urakawa
    • Journal Title

      Journal of Korean Mathematical Society

      Volume: 55 Pages: 1-22

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups2018

    • Author(s)
      S. Ohno, T. Sakai and H. Urakawa
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 48 Pages: 1-43

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Harmonic maps and biharmonic maps on principal bundles and warped products2018

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Journal of Korean Mathematical Society

      Volume: 55

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic vector fields on pseudo-Riemannian manifolds2018

    • Author(s)
      M. Markellos and H. Urakawa
    • Journal Title

      Journal of Geometry and Physics

      Volume: 130 Pages: 1-26

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic submanifolds in a Riemannian manifold2018

    • Author(s)
      Norihito Koiso and Hajime Urakawa
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 55

    • NAID

      120006478932

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Polyharmonic maps into the Euclidean space2018

    • Author(s)
      Nobumitsu Nakauchi and Hajime Urakawa
    • Journal Title

      Note di Matematica

      Volume: 38

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Rigidity of transversally biharmonic maps between foliated Riemannian manifolds2018

    • Author(s)
      Shinji Ohno, Takashi Sakai and Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 47

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] Biharmonic vector fields on pseudo-Riemannian manifolds2018

    • Author(s)
      Michael Markellos and Hajime Urakawa
    • Journal Title

      Journal of Geometry and Physics

      Volume: 130

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Journal Article] CR rigidity of pseudo harmonic maps and pseudo biharmonic maps2017

    • Author(s)
      H. Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 46 Pages: 141-187

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic submanifolds in a Riemannian manifold2017

    • Author(s)
      Norihito Koiso and Hajime Urakawa
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 69

    • NAID

      120006478932

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] CR rigidity of pseudo harmonic maps and pseudo biharmonic maps2017

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 46

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Rigidity of transversally biharmonic maps between foliated Riemannian manifolds2017

    • Author(s)
      Shinji Ohno, Takashi Sakai and Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 48

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] リーマン幾何、関数解析そしてアインシュタイン2017

    • Author(s)
      浦川 肇
    • Journal Title

      数理科学

      Volume: 646 Pages: 42-48

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Harmonic maps and bi-harmonic maps on CR-manifolds and foliated Riemannian manifolds2016

    • Author(s)
      Shinji Ohno, Takashi Sakai and Hajime Urakawa
    • Journal Title

      Journal of Applied Mathematics and Physics

      Volume: 4 Pages: 2272-2289

    • DOI

      10.4236/jamp.2016.412219

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic homogeneous hypersurfaces in compact symmetric spaces2015

    • Author(s)
      Shinji Ohno, Takashi Sakai, Hajime Urakawa
    • Journal Title

      Differential Geometry and its Applications

      Volume: 43 Pages: 155-179

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] The biharmonicity of sections of the tangent bundle2015

    • Author(s)
      M. Markellos and H. Urakawa
    • Journal Title

      Monatshefte fur Matematik

      Volume: 176 Pages: 1-12

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Harmonic Maps and Biharmonic Maps2015

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Symmetry

      Volume: 7 Pages: 651-674

    • DOI

      10.3390/sym7020651

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Sasaki manifolds, Kaehler cone manifolds and biharmonic submanifolds2015

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Illinois Journal of Mathematics

      Volume: 59 Pages: 1-17

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Geometry of Sasaki manifolds, Kaehler cone manifolds and bi-harmonic submanifolds2015

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Topology and its Applications

      Volume: 196 Pages: 1023-1032

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Triharmonic isometric immersions into a manifold of non-positively constant curvature2015

    • Author(s)
      Shun Maeta, Nobumitsu Nakauchi and Hajime Urakawa
    • Journal Title

      Monatsuhefte fur Matematiki

      Volume: 176 Pages: 1-20

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] The biharmonicity of sections of the tangent bundle2015

    • Author(s)
      Michael Markellos, Hajime Urakawa
    • Journal Title

      Monatsuheft fur Matematik

      Volume: 178 Pages: 389-404

    • DOI

      10.1007/s00605-014-0702-7

    • Peer Reviewed / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Bubbling phenomena of biharmonic maps2015

    • Author(s)
      Nobumitsu Nakauchi, Hajime Urakawa
    • Journal Title

      Journal of Geometry and Physics

      Volume: 98 Pages: 355-375

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] CR rigidity of pseudo harmonic maps and pseudo biharmonic maps2015

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematics Journal

      Volume: 44 Pages: 1-39

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Triharmonic isometric immersions into a manifold of non-positively constant curvature2015

    • Author(s)
      Shun Maeta, Nobumitsu Nakauchi and Hajime Urakawa
    • Journal Title

      Monatsh. Math.

      Volume: 未定 Pages: 551-567

    • DOI

      10.1007/s00605-014-0713-4

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25887044, KAKENHI-PROJECT-25400154, KAKENHI-PROJECT-15K17542
  • [Journal Article] Biharmonic maps into s Riemannian manifold of non-positive curvature2014

    • Author(s)
      H. Urakawa, N. Nakauchi and S. Gudmundsson
    • Journal Title

      Geometriae Dedicata

      Volume: 169 Pages: 263-272

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic maps into a Riemannian manifold of non-positive curvature2014

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Geometriae Dedicata

      Volume: 164 Pages: 1-10

    • DOI

      10.1007/s10711-013-9854-1

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207, KAKENHI-PROJECT-24540213
  • [Journal Article] Biharmonic maps into symmetric spaces and integrable systems2014

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 43 Pages: 105-136

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Conformal change of Riemannian metrics and biharmonic maps2014

    • Author(s)
      H. Urakawa and H. Naito
    • Journal Title

      Indiana University Mathematical Journal

      Volume: 63 Pages: 1-26

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic maps into a Riemannian manifold of non-positive curvature2014

    • Author(s)
      Nobumitsu Nakauchi, Hajime Urakawa and Sigmundur Gudmundsson
    • Journal Title

      Geometriae Dedicata

      Volume: 169 Pages: 263-272

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] The bienergy of unit vector fields2014

    • Author(s)
      H. Urakawa and M. Markellos
    • Journal Title

      Annals of Global Analysis and Geometry

      Volume: 46 Pages: 431-457

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Conformal change of Riemannian metrics and biharmonic maps2014

    • Author(s)
      Hisashi Naito and Hajime Urakawa
    • Journal Title

      Indiana University Mathematical Journal

      Volume: 63 Pages: 1631-1657

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic maps into compact Lie groups and integrable systems2014

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 43 Pages: 73-103

    • Peer Reviewed / Acknowledgement Compliant / Open Access
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic submanifolds in a Riemannian manifold with non-positive curvature2013

    • Author(s)
      H. Urakawa and N. Nakauchi
    • Journal Title

      Results in Mathematics

      Volume: 63 Pages: 467-474

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic Lagrangian submanifolds in Kaehler manifolds2013

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Glasgow Mathematical Journal

      Volume: 55 Pages: 465-480

    • DOI

      10.1017/s0017089512000730

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Biharmonic maps into compact Lie groups and integrable systems2013

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 42 Pages: 1-26

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Biharmonic hypersurfaces in a Riemannian manifold with non-positive Ricci curvature2013

    • Author(s)
      H.Urakawa and N. Nakauchi
    • Journal Title

      Annals of Global Analysis and Geometry

      Volume: Vol. 40 Pages: 125-131

    • DOI

      10.1007/s10455-011-9249-1

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207, KAKENHI-PROJECT-23540091
  • [Journal Article] Biharmonic Lagrangean submanifolds in Kaehler manifolds2013

    • Author(s)
      H. Urakawa and S. Maeta
    • Journal Title

      Glasgow Mathematical Journal

      Volume: 55 Pages: 465-480

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Journal Article] Biharmonic submanifolds in a Riemannian manifolds with non-positive curvature2013

    • Author(s)
      H. Urakawa and N. Nakauchi
    • Journal Title

      Results in Mathematics

      Volume: Vol. 63 Pages: 467-474

    • DOI

      10.1007/s00025-011-0209-7

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207, KAKENHI-PROJECT-23540091, KAKENHI-PROJECT-24540213
  • [Journal Article] Biharmonic maps into symmetric spaces and integrable systems2013

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 42 Pages: 1-28

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Biharmonic submanifolds in a Riemannian manifold with non-positive curvature2012

    • Author(s)
      H.Urakawa
    • Journal Title

      Results in Math.

      Volume: (未定)(掲載決定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] 「教育数学の構築」を目指して2012

    • Author(s)
      浦川 肇
    • Journal Title

      数理解析研究所講究録

      Volume: 1801 Pages: 20-30

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Biharmonic hypersurfaces in a Riemannian manifold with non-positive curvatvire2011

    • Author(s)
      H.Urakawa
    • Journal Title

      Annals of Global Analysis and Geometry

      Volume: 未定(発表受理印刷中)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Classifications and isolation phenomena of biharmonic maps andbi-Yang-Mills fields2011

    • Author(s)
      H.Urakawa
    • Journal Title

      Note di Matematica

      Volume: 未定(発表受理印刷中)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Computer visions for the eigenvalue problems of embedded surfaces and plane domains, Annal2011

    • Author(s)
      H. Urakawa, and M. Jumonji
    • Journal Title

      Stiintifice Ale Universitaii "Al. I. Cuza" Din Iasi

      Volume: Vol. 57 Pages: 125-136

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] The geometry of biharmonic maps, Contemporary Mathematics2011

    • Author(s)
      H. Urakawa
    • Journal Title

      Amer. Math. Soc

      Volume: Vol. 542 Pages: 159-175

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] The geometry of biharmonic maps2011

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, American Mathematical Society

      Volume: 未定(発表受理印刷中)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Biharmonic maps into compact Lie groups and symmetric spaces, Proceedings Amer2011

    • Author(s)
      H. Urakawa
    • Journal Title

      Institute Physics

      Volume: Vol.1329 Pages: 246-263

    • DOI

      10.1063/1.3546089

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Biharmonic maps into compact Lie groups, and symmetric spaces2011

    • Author(s)
      H.Urakawa
    • Journal Title

      American Institute of Physics, Conference Proceedings

      Volume: 1329 Pages: 246-263

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Computer visions for the eigenvalue problems of embedded surfaces and plane domains2011

    • Author(s)
      H.Urakawa
    • Journal Title

      Analele Stiintifice Ale Universitatii Al.I.Cuza Din Iasi (Serie Noua) Matematica

      Volume: 57 Pages: 125-136

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Proiectively flat connections and flat connections on homogeneous spaces2010

    • Author(s)
      H.Urakawa
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 39 Pages: 139-155

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Classification and iso-lation phenomena of bi-harmonic maps and bi-Yang-Mills fields2010

    • Author(s)
      T. Ichiyama, J. Inoguchi, H. Urakawa
    • Journal Title

      Note di Matematica (印刷中)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Journal Article] Affine Weyl groups and the boundary value eigenvalue problems of the Laplacian2010

    • Author(s)
      Yoshinori Hoshikawa, Hajime Urakawa
    • Journal Title

      Interdiscip.Inform.Sci.

      Volume: 16 Pages: 93-109

    • NAID

      110009794882

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Projectively flat connections and flat connections on homogeneous spaces2010

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Hokkaido Math.J.

      Volume: 39 Pages: 139-155

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Classifications and isolation phenomerna of bi-harmonic maps andbi-Yang-Mills fields2010

    • Author(s)
      H. Urakawa, T. Ichiyama and J.Inoguchi
    • Journal Title

      Note di Matematica

      Volume: Vol. 30 Pages: 15-48

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Classifications and isolation phenomena of bi-harmonic maps and bi-Yang-Mills fields2010

    • Author(s)
      T.Ichiyama, J.Inoguchi, H.Urakawa
    • Journal Title

      Note di Matematica (In press)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Journal Article] Affine Weyl groups and the boundary value eigenvalue problems of the Laplacian, Interdiscip2010

    • Author(s)
      Y. Hoshikawa and H. Urakawa
    • Journal Title

      Inform. Sci.

      Volume: 16 Pages: 93-109

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Affine Weyl Groups and the Boundary Value Eigenvalue Problems of the Laplacian2010

    • Author(s)
      H. Urakawa and Y. Hosikawa
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: Vol. 16 Issue: 1 Pages: 93-109

    • DOI

      10.4036/iis.2010.93

    • NAID

      130000250325

    • ISSN
      1340-9050, 1347-6157
    • Language
      English
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Affine Weyl groups and the boundary value eigenvalue problems of the Laplacian2010

    • Author(s)
      H.Urakawa
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: 16 Pages: 93-109

    • NAID

      110009794882

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Projectively flat connections and flat connections on homogeneous spaces2010

    • Author(s)
      H. Urakawa
    • Journal Title

      Hokkaido Math. J.

      Volume: Vol. 39 Pages: 139-155

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Compactness of the moduli space of solutions of the Seiberg-Witten egations over higher dimensional compact Kaehler manifolds.2009

    • Author(s)
      H.Urakawa
    • Journal Title

      Publicatione Mathematicae Debrecen 74

      Pages: 433-480

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Convergence rates to optimal distribution of the Boltzmann machine on simulated annealing2009

    • Author(s)
      H. Urakawa
    • Journal Title

      Interdiscip. Inform. Sci

      Volume: 15 Pages: 291-299

    • NAID

      110007317875

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] The eigenvalue problems on compact embedded surfaces and three dimensional bounded domains2009

    • Author(s)
      M. Jumonji and H. Urakawa
    • Journal Title

      Interdisciplinary Information Sciences 14

      Pages: 191-223

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Compactness of the moduli space of solutions of the Seiberg-Witten equations over higher dimensional Kaehler manifolds2009

    • Author(s)
      H. Urakawa
    • Journal Title

      Publ. Math.Debrecen

      Volume: Vol. 74 Pages: 433-480

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Ray-Singer zeta function for compact flat manifolds2009

    • Author(s)
      T.Sunada, H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer. Math. Soc. 484

      Pages: 287-294

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Ray-Singer zeta functions for compact flat manifolds2009

    • Author(s)
      Toshikazu Sunada, Hajime Urakawa
    • Journal Title

      Contemp.Math. 484

      Pages: 287-294

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Classification and isolation phenomena of bi-harmonic maps and bi-Yang-Mills fields2009

    • Author(s)
      T. Ichiyama, J. Inoguchi and H. Urakawa
    • Journal Title

      Note di Matematica (In press)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Ray-Singer zeta functions for compact flat manifolds2009

    • Author(s)
      H. Urakawa nad T. Sunada
    • Journal Title

      Contemporary Math. Amer. Math. Soc

      Volume: Vol. 484 Pages: 287-294

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Bi-harmonic maps and bi-Yang-Mills fields2009

    • Author(s)
      H. Urakawa, T. Ichiyama and J. Inoguchi
    • Journal Title

      Note di Matematica

      Volume: 28 Pages: 233-275

    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Convergence Rates to Optimal Distribution of the Boltzmann Machine on Simulated Annealing2009

    • Author(s)
      H. Urakawa
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: Vol. 15 Issue: 2 Pages: 291-299

    • DOI

      10.4036/iis.2009.291

    • NAID

      110007317875

    • ISSN
      1340-9050, 1347-6157
    • Language
      English
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Visualization of the eigenvalue problems of the Laplacian for embedded- surfaces and its applications2009

    • Author(s)
      H. Urakawa, M. Jumonji
    • Journal Title

      Aspects analytiques de la geometrie Riemannienne, Serie Seminaire et Congres (未定)掲載確定

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Journal Article] The eigenvalues of the Laplacian on compact embeded surfaces and three dimensional bounded domains2009

    • Author(s)
      H. Urakawa
    • Journal Title

      Interdisciplinary Information Sciences (未定)掲載確定

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Journal Article] Compactness of the moduli space of solutions of the Seiberg-Witten equations over higher dimensional compact Kahler manifolds2009

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Publ.Math.Debrecen 74

      Pages: 433-480

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Convergence rates to optimal distribution of the Boltzmann machine on simulated annealing2009

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Interdiscip.Inform.Sci. 15

      Pages: 291-299

    • NAID

      110007317875

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Convergence rates to optimal distribution of the Boltzmann machine on simurated annealing2009

    • Author(s)
      H.Urakawa
    • Journal Title

      Interdisciplinary Information Sciences 15

      Pages: 291-299

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Journal Article] Bi-harmonic maps and bi-Yang-Mills fields2009

    • Author(s)
      T. Ichiyama, J. Inoguchi, H. Urakawa
    • Journal Title

      Note di Matematica Vol.28

      Pages: 233-275

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Journal Article] Bi-harmonic maps and bi-Yang-Mills fields (in print)2008

    • Author(s)
      H. Urakawa-T. Ichiyama-J. Inoguchi
    • Journal Title

      Note di Matematica (掲載確定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Journal Article] Visualization of the eigenvalue problems of the Laplacian for embedded surfaces and its applications2008

    • Author(s)
      M. Jumonji and H. Urakawa
    • Journal Title

      Serie Seminaire et Congre, Soc. Math. France 19

      Pages: 47-91

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Journal Article] Visualization of the eigenvalue problems of the Laplacian for embedded surfaces and its applications2007

    • Author(s)
      H.Urakawa
    • Journal Title

      The Proceedings of Socie Math. de France (印刷決定)

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Bi-harmonic maps and bi-Yang Mills fields2007

    • Author(s)
      H. Urakawa
    • Journal Title

      Note di Matematica (掲載決定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18540154
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana University Mathematical Journal 55

      Pages: 259-288

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana Univ. Math. J. 55

      Pages: 259-288

    • Data Source
      KAKENHI-PROJECT-18540154
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H. Urakawa
    • Journal Title

      Indiana Univ. Math. J. 55

      Pages: 259-288

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17340043
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana Univ.Math.J. (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] 高次元ケーラー多様体上のサイバーグ・ウィッテン理論2006

    • Author(s)
      浦川 肇
    • Journal Title

      研究集会「大阪大学微分幾何研究集会」報告集

      Pages: 95-99

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills fields on CR manifolds2006

    • Author(s)
      E. Barletta, S. Dragomir, and H. Urakawa
    • Journal Title

      J. Math. Phys. 47, 083504

      Pages: 41-41

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17340043
  • [Journal Article] Yang-Mills fields on CR manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Journal of Mathematical Physics 47

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] 朝倉書店2006

    • Author(s)
      浦川 肇
    • Journal Title

      微積分の基礎

      Pages: 232-232

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana University Mathematical Journal 55(1)

      Pages: 259-288

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Indiana University Mathematical Journal (印刷中)

    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Yang-Mills fields on CR manifolds.2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Journal of Mathematical Physics Vol. 47

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H. Urakawa
    • Journal Title

      Indiana University Mathematical Journal (印刷中)

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana University Mathematical Journal (to appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-14340021
  • [Journal Article] Convergence rates to equilibrium of the heat Kernels on compact Riemannian manifolds.2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana University Mathematical Journal Vol. 55

      Pages: 259-288

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana Univ. Math. J. (In press)

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Yang-Mills field on CR manifolds2006

    • Author(s)
      H.Urakawa
    • Journal Title

      Journal of Mathematical Physics 47(8)

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills fields analogue of biharmonic maps.2005

    • Author(s)
      H.Urakawa
    • Journal Title

      Topics in almost Hermitian geometry and related fields

      Pages: 41-49

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] 数学と工学との出会い--連続系を中心に--2005

    • Author(s)
      浦川 肇
    • Journal Title

      数学の楽しみ 冬号

      Pages: 122-137

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills fields analogue of biharmonic maps2005

    • Author(s)
      Cornelia-Livia Bejan, Hajime Urakawa
    • Journal Title

      Topics Hermitian Geometry and Related Fields, World Scientific

      Pages: 41-49

    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Visualization of the eigenvalues and eigenfunctions for the Laplacian on compact embedded surfaces with or without boundaries2005

    • Author(s)
      H. Urakawa
    • Journal Title

      Proceedings of International Workshop on Integrable Systems Geometry and Visualization

      Pages: 29-79

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills fields analogue of biharmonic maps2005

    • Author(s)
      H.Urakawa
    • Journal Title

      Topics in almost Hermitian geometry and related fields

      Pages: 41-49

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills fields analogue of biharmonic maps2005

    • Author(s)
      H. Urakawa
    • Journal Title

      Topics Hermitian Geometry and Related Fields

      Pages: 41-49

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer.Math.Soc. 348

      Pages: 221-232

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The heat kernel and the Green kernel of an infinite graph2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemp. Math. 2004

      Pages: 245-258

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] The heat kernel and the Green kernel of an infinite graph2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer. Math. Soc. 347

      Pages: 245-258

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The heat kernel and the Green kernel of an infii graph.2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer.Math.Soc. Vol.347

      Pages: 245-258

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills connections in homogeneous principal fiber bundles2004

    • Author(s)
      J-S.Park, H.Urakawa
    • Journal Title

      International J.Pure Appl.Math. 10

      Pages: 79-90

    • Data Source
      KAKENHI-PROJECT-14340021
  • [Journal Article] Yang-Mills theory over compact symplectic manifolds2004

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Annals Global Analysis Geometry 25

      Pages: 365-402

    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Yang-Mills theory over compact symplectic manifolds2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Annals of Global Analysis and Geometry 25

      Pages: 365-402

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemp.Math. 348

      Pages: 221-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Yang-Mills connections in homogeneous principal fiber bundles2004

    • Author(s)
      H.Urakawa
    • Journal Title

      International J.Pure Applied Mathematics 10

      Pages: 79-90

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Math., AMS 348

      Pages: 221-232

    • Data Source
      KAKENHI-PROJECT-14340021
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory.2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer.Math.Soc. Vol.348

      Pages: 221-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills theory over compact symplectic manifolds.2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Annals of Global Analysis and Geometry Vol.25

      Pages: 365-402

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills theory over compact symplectic manifolds2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Annals Global Analysis Geometry 25

      Pages: 365-402

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] Yang-Mills theory over compact symplectic manifolds2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Annals Global Analysis Geometry 25

      Pages: 365-402

    • Data Source
      KAKENHI-PROJECT-14340021
  • [Journal Article] Yang-Mills connections in homogeneous principal fiber bundles2004

    • Author(s)
      J-S.Park, Hajime Urakawa
    • Journal Title

      International J.Pure Appl.Math. 10

      Pages: 79-90

    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] The heat kernel and Green kernel of an infinite graph2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer.Math.Soc. 347

      Pages: 245-258

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The heat kernel and Green kernel of an infinite graph2004

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Contemporary Math. 347

      Pages: 245-258

    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] The heat kernel and the Green kernel of an infinite graph2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemp.Math. 347

      Pages: 245-258

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] 数学と工学との出会い--離散系を中心に--2004

    • Author(s)
      浦川 肇
    • Journal Title

      数学通信 第9巻 No.3

      Pages: 5-17

    • NAID

      40006493219

    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory2004

    • Author(s)
      Hajime Urakawa
    • Journal Title

      Contemporary Math. 348

      Pages: 221-232

    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemporary Mathematics, Amer. Math. Soc. 348

      Pages: 221-232

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Journal Article] The Dirichlet eigenvalue problem, the finite element method and graph theory2004

    • Author(s)
      H.Urakawa
    • Journal Title

      Contemp. Math. 348

      Pages: 221-232

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] The Cheeger constant, the heat kernel, and the Green kernel of an infinite graph2003

    • Author(s)
      H.Urakawa
    • Journal Title

      Monatsh.Math. 138

      Pages: 225-237

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] The Cheeger constant, the heat kernel, and the Green kernel of an infinite graph2003

    • Author(s)
      H.Urakawa
    • Journal Title

      Monatsh. Math. 138

      Pages: 225-237

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-15340039
  • [Journal Article] Convergence rates to equilibrium of the heat kernels on compact Riemannian manifolds

    • Author(s)
      H.Urakawa
    • Journal Title

      Indiana University Mathematical Journal (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-14340021
  • [Patent] 有限要素法直接計算プログラムおよび解析方法2005

    • Inventor(s)
      浦川肇、十文宇正樹
    • Industrial Property Rights Holder
      浦川肇、十文宇正樹
    • Industrial Property Number
      2005-134794
    • Filing Date
      2005-05-06
    • Data Source
      KAKENHI-PROJECT-16340044
  • [Presentation] Harmonic maps and biharmonic maps between Riemannian manifolds2022

    • Author(s)
      Hajime Urakawa
    • Organizer
      The 2022 the First International Conference on Applied Mathematics and Digital Simulation (AMDS 2022)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] 調和写像と2調和写像の幾何学2019

    • Author(s)
      浦川肇
    • Organizer
      第18回秋葉原微分幾何学セミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] Biharmonic principal G-bundles and vector bundles2019

    • Author(s)
      Hajime Urakawa
    • Organizer
      Differential Equations over Manifolds
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] Geometry of harmonic maps and biharmonic maps2019

    • Author(s)
      Hajime Urakawa
    • Organizer
      International conference of differential geometry
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] Harmonic and/or biharmonic submersions2018

    • Author(s)
      Hajime Urakawa
    • Organizer
      Differential Geometry Workshop 2018 at Cagliari, Italy
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic and biharmonic Riemannian submersions2018

    • Author(s)
      Hajime Urakawa
    • Organizer
      Differential Geometry Workshop 2018--Harmonic maps, biharmonic maps, harmonic morphisms and related topics--
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] On biharmonic Riemannian submersions2018

    • Author(s)
      浦川肇
    • Organizer
      福岡大学微分幾何研究会
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] Biharmonic maps and harmonic morphisms from Riemannian manifolds of positive sectional curvature2018

    • Author(s)
      浦川肇
    • Organizer
      北海道大学研究集会「幾何学のスペクトル Spectrum of Geometry」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] Biharmonic Riemannian submersions の幾何2018

    • Author(s)
      浦川肇
    • Organizer
      研究会「多様体上の微分方程式」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03352
  • [Presentation] カード・シャッフル、焼き鈍し、そして離散幾何解析2017

    • Author(s)
      浦川 肇
    • Organizer
      東京研究会「離散グラフのスペクトル解析とその応用」
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic and biharmonic immersions and submersions2017

    • Author(s)
      Hajime Urakawa
    • Organizer
      Harmonic Map Workshop
    • Place of Presentation
      l'Aber Wrac'h, Brest, France
    • Year and Date
      2017-05-15
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic and biharmonic immersions and submersions2017

    • Author(s)
      浦川 肇
    • Organizer
      第16回多様体上の微分方程式研究会
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic and biharmonic immersions and submersions2017

    • Author(s)
      Hajime Urakawa
    • Organizer
      the Harmonic Map Workshop at Brest, France
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic and biharmonic immersions and submersions2017

    • Author(s)
      Hajime Urakawa
    • Organizer
      Seminar at the Korean Institute for Advanced Studies
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic maps and biharmonic maps on the warped product2017

    • Author(s)
      浦川 肇
    • Organizer
      小磯憲史先生退職記念研究集会
    • Place of Presentation
      大阪大学理学研究科
    • Year and Date
      2017-03-13
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of biharmonic maps and harmonic maps2016

    • Author(s)
      Hajime Urakawa
    • Organizer
      2016 Workshop on Geometry and Related Topics
    • Place of Presentation
      Jeju National University, Korea
    • Year and Date
      2016-01-14
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of biharmonic mappings and CR geometry2016

    • Author(s)
      Hajime Urakawa
    • Organizer
      Conference "CR geometry and PDE's, VII, dedicated to the memory of Giuseppe Zampieri"
    • Place of Presentation
      Levico Terme, Trento, Italy
    • Year and Date
      2016-06-26
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Biharmonic maps on principal G-bundles over Riemannian manifolds with negative Ricci curvature2016

    • Author(s)
      浦川 肇
    • Organizer
      研究集会「多様体上の微分方程式」
    • Place of Presentation
      金沢大学サテライトプラザ
    • Year and Date
      2016-11-17
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Biharmonic maps on principal G-bundles2016

    • Author(s)
      浦川 肇
    • Organizer
      部分多様体論・湯沢2016
    • Place of Presentation
      湯沢グランド・ホテル
    • Year and Date
      2016-12-01
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] コンパクト Lie 群内の二重調和等質超曲面の構成2016

    • Author(s)
      大野晋司、酒井高司、浦川 肇
    • Organizer
      日本数学会2016年秋季総合分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Biharmonic maps on principal G-bundles over Riemannian manifolds of negative Ricci curvature2016

    • Author(s)
      浦川 肇
    • Organizer
      2016年度福岡大学微分幾何研究会
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2016-11-03
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] コンパクト対称空間内の二重調和超曲面2015

    • Author(s)
      大野晋司、酒井高司、浦川 肇
    • Organizer
      日本数学会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Harmonic maps and biharmonic maps2014

    • Author(s)
      浦川 肇
    • Organizer
      大阪市立大学微分幾何セミナー
    • Place of Presentation
      大阪市立大学理学部
    • Year and Date
      2014-10-22
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of bi-harmonic maps and k-harmonic maps2014

    • Author(s)
      H. Urakawa
    • Organizer
      Conference on Geometry
    • Place of Presentation
      Galatasaray University, Istanbul, Turkey
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of harmonic maps, and biharmonic maps2014

    • Author(s)
      H. Urakawa
    • Organizer
      Seminar in Differential Geometry
    • Place of Presentation
      Korean Institute for Advanced Study
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geomerry of harmonic maps and biharmonic maps2013

    • Author(s)
      浦川 肇
    • Organizer
      山口大学幾何学研究会2013「進展する曲面論」
    • Place of Presentation
      山口大学理学部
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] k-調和写像と B-Y. Chen 予想の当面する課題2013

    • Author(s)
      浦川 肇
    • Organizer
      研究集会「多様体上の微分方程式」
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of harmonic maps, bi-harmonic maps and integrable systems2013

    • Author(s)
      H. Urakawa
    • Organizer
      International Conference on Topology and Geometry, 2013
    • Place of Presentation
      島根大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] k-調和写像の幾何と解析2013

    • Author(s)
      浦川 肇
    • Organizer
      Geometry and Something, 福岡大学幾何学研究会
    • Place of Presentation
      福岡大学セミナーハウス
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of harmonic maps, biharmonic maps and integrable systems2013

    • Author(s)
      H. Urakawa
    • Organizer
      Differential Geometry Seminar at Iasi University
    • Place of Presentation
      Iasi University, Iasi, Romania
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] Geometry of harmonic maps, bi-harmonic maps into compact Lie groups and/or symmetric spaces2013

    • Author(s)
      H. Urakawa
    • Organizer
      Differential Geometry Seminar at Basilicata University
    • Place of Presentation
      ¨niversity of Basilicata, Potenza, Italy
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] 非正曲率リーマン多様体への2-調和写像2012

    • Author(s)
      浦川肇・中内伸光
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大学神楽坂校舎
    • Year and Date
      2012-03-28
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Geometry of biharmonic maps: L^2-rigidity, biharmonic Lagrangian submanifolds of Kaehler manifolds, and conformal change of metrics2012

    • Author(s)
      Hajime Urakawa
    • Organizer
      The 3rd International Colloquium on Differential Geometry and its Related Fields
    • Place of Presentation
      Veriko Tarnovo, Bulgaria
    • Invited
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Geometry of biharmonic maps-existence, non-existenceand classification problems of proper biharmonic maps2012

    • Author(s)
      H. Urakawa
    • Organizer
      The 3^<rd> International Colloquium on Differential Geometry and its Related Topics
    • Place of Presentation
      Veliko Tarnovo Univ., Bulgaria
    • Year and Date
      2012-09-05
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] 2-調和写像の除去可能特異点定理とバブリング2012

    • Author(s)
      浦川肇・中内伸光
    • Organizer
      日本数学会
    • Place of Presentation
      東京理科大学神楽坂校舎
    • Year and Date
      2012-03-28
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Geometry of biharmonic maps-Chen's conjecture,biharmonic submanifolds of Kaehler manifods2012

    • Author(s)
      浦川 肇
    • Organizer
      多様体上の微分方程式
    • Place of Presentation
      金沢大学サテライトプラザ
    • Invited
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Biharmonic maps into a Riemannian manifold of non-positive curvature and B.Y. Chen's conjecture2011

    • Author(s)
      浦川 肇
    • Organizer
      金沢大域解析研究会
    • Place of Presentation
      金沢大学
    • Year and Date
      2011-11-10
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Biharmonic maps into a Riemannian manifold of non-positive curvature and B.Y. Chen's conjecture2011

    • Author(s)
      浦川 肇
    • Organizer
      松江微分幾何研究会
    • Place of Presentation
      島根大学
    • Year and Date
      2011-12-17
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Biharmonic maps into compact Lie groups and symmetric spaces, The "Alexandru Myller" Mathematical Seminar Centennial Conference2010

    • Author(s)
      H. Urakawa
    • Organizer
      Iasi University
    • Place of Presentation
      Romania
    • Year and Date
      2010-06-25
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Geometry of biharmonic maps and harmonic maps2010

    • Author(s)
      H.Urakawa
    • Organizer
      Alexandru Myller Mathematical SeminarCentennial Conference
    • Place of Presentation
      ルーマニア、ヤシ大学
    • Year and Date
      2010-06-24
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Biharmonic maps into compact Lie groups and the integrable systems2009

    • Author(s)
      H.Urakawa
    • Organizer
      International conference on Harmonic Maps
    • Place of Presentation
      Cagliari Univ. Italy
    • Year and Date
      2009-09-08
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Presentation] Biharmonic maps into compact Lie groups and the integrable systems2009

    • Author(s)
      H. Urakawa
    • Organizer
      In: International conference on Harmonic Maps-in honor of sixtieth birthday of Professor John Wood
    • Place of Presentation
      Cagliari University, (Italy)
    • Year and Date
      2009-09-08
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Presentation] Geometry of biharmonic maps, Conference of harmonic maps-in honor of Professor2009

    • Author(s)
      H. Urakawa
    • Organizer
      J. Wood's sixtieth birthday
    • Place of Presentation
      Cagliari, Italy
    • Year and Date
      2009-09-08
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] Geometry of bi-harmonic maps2009

    • Author(s)
      H.Urakawa
    • Organizer
      Conference of harmonic maps-in honor of Professor J.Wood in his sixtieth birthday
    • Place of Presentation
      Cagliari University, Italy
    • Year and Date
      2009-09-08
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] Geometry of biharmonic maps2009

    • Author(s)
      浦川肇
    • Organizer
      Conference of harmonic maps--in honor of Professor J.Wood's sixtieth birthday
    • Place of Presentation
      Cagliari, Italy
    • Year and Date
      2009-09-08
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] Geometry of biharmonic maps--existence, classification, regularity, bubbling2009

    • Author(s)
      浦川肇
    • Organizer
      福岡大学微分幾何研究会
    • Place of Presentation
      福岡大学
    • Year and Date
      2009-11-22
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] The geometry of biharmonic maps, A Harmonic Map Fest in honor of John C2009

    • Author(s)
      H. Urakawa
    • Organizer
      Wood's 60th Birthday, CagliariUniversity
    • Place of Presentation
      Italy
    • Year and Date
      2009-09-09
    • Data Source
      KAKENHI-PROJECT-21540207
  • [Presentation] 2-調和写像の幾何-存在、分類問題2009

    • Author(s)
      浦川肇
    • Organizer
      多様体上の大域解析学研究会
    • Place of Presentation
      呉羽ハイツ(富山市)
    • Year and Date
      2009-10-31
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] Conformal Geometry, Harmonic Maps and Biharmonic Maps2008

    • Author(s)
      浦川肇
    • Organizer
      研究集会「Geometry and Something」
    • Place of Presentation
      福岡大学セミナーハウス
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] 共形幾何学とbiharmonic maps2008

    • Author(s)
      浦川肇
    • Organizer
      研究集会「多様体上の微分方程式」
    • Place of Presentation
      金沢市いしかわシティカレッジ
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] アファイン・ワイル群とラプラシアンの境界値固有値問題(星川良紀と共同)2008

    • Author(s)
      浦川肇
    • Organizer
      日本数学会2008年度秋季総合分科会、幾何学分科会
    • Place of Presentation
      東京工業大学
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] Conformal geometry, harmonic maps and biharmonic maps2008

    • Author(s)
      H. Urakawa
    • Organizer
      In: International conference on "Conformal Geometry: Invariant theory and the variational method"
    • Place of Presentation
      Roscoff (France)
    • Year and Date
      2008-07-02
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Presentation] Conformal Geometry, Harmonic Maps and Biharmonic Maps2008

    • Author(s)
      H. Urakawa
    • Organizer
      International Conference of Conformal Geometry-Invariant Theory and Variational Method
    • Place of Presentation
      Roscoff, France
    • Data Source
      KAKENHI-PROJECT-20340025
  • [Presentation] Bi-harmonic maps and bi-Yang-Mills fields-新しい変分問題2007

    • Author(s)
      浦川肇
    • Organizer
      第54回幾何学シンポジウム
    • Place of Presentation
      鹿児島大学(鹿児島県)
    • Year and Date
      2007-08-24
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Presentation] Biharmonic maps and bi-Yang-Mills fields2007

    • Author(s)
      H. Urakawa
    • Organizer
      In: International conference "ADVANCES IN DIFFERENTIAL GEOMETRY" in honor of Professor Oldrich Kowalski
    • Place of Presentation
      Lecce (Italy)
    • Year and Date
      2007-06-13
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Presentation] Bi-harmonic and bi-Yang-Mills fields2007

    • Author(s)
      H. Urakawa
    • Organizer
      International Conference, Recent advances in Differential Geometry in honor of Prof. O. Kowalski
    • Place of Presentation
      Lecce, Italy
    • Year and Date
      2007-06-14
    • Data Source
      KAKENHI-PROJECT-19204004
  • [Presentation] CR geometry, pseudo harmonic maps and pseudo biharmonic maps

    • Author(s)
      浦川 肇
    • Organizer
      福岡大学微分幾何学研究会
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2014-10-30 – 2014-11-03
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] CR analogue of harmonic maps and biharmonic maps

    • Author(s)
      浦川 肇
    • Organizer
      多様体上の微分方程式研究会
    • Place of Presentation
      石川四高記念館-しいのき迎賓館
    • Year and Date
      2014-11-20 – 2014-11-22
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] 2重調和部分多様体--B.Y. Chen 予想について--

    • Author(s)
      小磯憲史(大阪大学理学研究科)、浦川 肇
    • Organizer
      第61回幾何学シンポジウム
    • Place of Presentation
      名城大学
    • Year and Date
      2014-08-23 – 2014-08-26
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] 2重調和部分多様体

    • Author(s)
      浦川 肇, 小磯憲史
    • Organizer
      日本数学会, 幾何学分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-27
    • Data Source
      KAKENHI-PROJECT-25400154
  • [Presentation] CR rigidity of pseudo harmonic maps and pseudo biharmonic maps

    • Author(s)
      Hajime Urakawa
    • Organizer
      Differential Geometry Seminar at Bisilicata University
    • Place of Presentation
      Basilicata University
    • Year and Date
      2014-09-09 – 2014-09-16
    • Invited
    • Data Source
      KAKENHI-PROJECT-25400154
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