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Katsuda Atsushi  勝田 篤

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KATSUDA ATSUSHI  勝田 篤

KATSUDA Atsushi  勝田 篤

勝田 篤  カツダ アツシ

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Researcher Number 60183779
Other IDs
External Links
Affiliation (Current) 2025: 慶應義塾大学, 自然科学研究教育センター(日吉), 訪問教授
2025: 九州大学, 数理学研究院, 名誉教授
Affiliation (based on the past Project Information) *help 2024: 慶應義塾大学, 自然科学研究教育センター(日吉), 訪問教授
2018 – 2022: 九州大学, 数理学研究院, 教授
2012: 九州大学, 数理(科)学研究科(研究院), 教授
2012: 九州大学, 数理学研究院, 教授
2010 – 2011: 九州大学, 大学院・数理学研究院, 教授 … More
2007 – 2009: Okayama University, Grad. School of Nat. Sci. Tech, Assoc. Prof
2007: Okayama University, Graduate School of Natural Science and Technology, Associate Professor
2006 – 2007: 岡山大学, 理学部, 准教授
2005 – 2006: OKAYAMA UNIVERSITY, Department of Mathematics, Associate Professor, 大学院・自然科学研究科, 助教授
2005 – 2006: 岡山大学, 大学院自然科学研究科, 助教授
1996 – 2006: 岡山大学, 理学部, 助教授
2001: Okayama University, Faculty of Science, Associate Professor, 理学部, 助教授
1993 – 1994: 岡山大学, 理学部, 助教授
1990: 岡山大学, 理学部, 助教授
1988: 岡山大学, 理学部, 助教授 Less
Review Section/Research Field
Principal Investigator
Geometry / Geometry / Basic Section 11020:Geometry-related
Except Principal Investigator
Geometry / Geometry / Global analysis / 代数学・幾何学 / Basic analysis / Global analysis / Basic analysis / Algebra / 解析学 / Algebra
Keywords
Principal Investigator
逆問題 / 安定性 / スペクトル / 熱核 / スペクトル逆問題 / inverse problem / 素閉測地線 / 漸近挙動 / heat kernel / 半古典近似 … More / ハイゼンベルグ群 / 酔歩 / べき零群 / stability / 境界距離 / 密度定理 / 双曲力学系 / ラプラシアン / グラフのラプラシアン / 非可換Bloch理論 / キリングベクトル場 / リッチ曲率 / 漸近展開 / 素測地線 / 離散べき零群 / closed geodesic / Heisenberg / Asymptotic formulas / Floquet-Bloch / boundary distance / spectre / nilpotent / random walk / べき零 / Gromov-Hausdorff convergence / Inverse spectral Problem / nilpotent groups / random walks / ハーパー作用素 / グロモフハウスドルフ収束 / ランダムウォーク / isoperimetric constants / isospectral graphs / Laplacian / the Hausdorff distance / spectrum / 等周定数 / 等スペクトルグラフ / ハウスドルフ距離 / グロモフハウドルフ距離 / 閉測地線 / 負曲率多様体 / 閉軌道 / 距離関数 / グロモフ-ハウスドルフ距離 / スペクトル収束 / 算術級数定理 / Yamabe型方程式 / 特異摂動 … More
Except Principal Investigator
リーマン多様体 / Aharonov-Bohm effect / 測地線 / 散乱振幅 / アハラノフ・ボーム効果 / integrated semigroup / scattering by magnetic field / Pauli operator / Dirac operator / Riemannian manifolds / カットローカス / リウヴィル多様体 / 共役跡 / 楕円体 / 可積分測地流 / 磁場散乱 / 曲率 / dissipativity condition / subtangential condition / semigroup of Lipschitz operators / Integrable geodesic flow / Liouville manifold / resonance at zero energy / リプシッツ作用素半群 / regularized semigroup / magnetic scattering / Distance functions / 距離関数 / graph / スペクトル / グラフ / P-調和写像 / resolvent convergence / 磁場による散乱 / 磁場をもつシュレディンガー作用素 / scattering by magnetic fields / パウリ作用素 / 閉測地線 / ellipsoid / conjugate locus / cut locus / スペクトル理論 / シュレディンガー作用素 / 散乱理論 / 写像類群 / 組紐群 / タイヒミュラー空間 / リーマン面の被覆 / 比較定理 / Hermite-Liouville / Kahler-Liouville / Cusp / Conjugate locus / Cut locus / Ellipsoid / エルミート・リウヴィル多様化 / ケーラー・リウヴィル多様体 / カスプ / 可積化測地流 / Cut loci / Geodesics / Morse theory / 切断跡 / モース理論 / Riemannian manifold / p-harmonic map / p-harmonic function / p-harmonic morphism / p-ラプラシアン / 幾何学 / p-調和関数 / p-調和写像 / approximation theorem for semigroups of operators / stability condition / wellposedness in the sense of Hadamard / evolution equation / abstract Cauchy problem / infinitesimal generator / comparison function / semigroup of lipschitz operators / well-posedness / non-densely defined operator / Wentzell boundary condition / acoustic boundary condition / semilinear evolution equation / quasilinear evolution equation / Chernoff's product formula / metric-like functional / fractional power / analytic semigroup / perturbation / Hadamard wellposedness / quasilinear equation / semilinear equation / semigroup of operators / 作用素半群の近似定理 / 安定性条件 / 消散条件 / 劣接線条件 / アダマールの意味の適切性 / 発展方程式 / quadratic surface / tri-axial ellipsoid / Jacobi / 双曲面 / 射影同値 / 極 / リウヴィル曲面 / 共役蹠 / 2次曲面 / 楕円面 / ヤコビ / spectral theory / point-like magnetic field / Aharonov-Bohm field / Trotter-Kato product formula / zero energy resonance / Feynman-Kac formula / Pauli operators / Dirac operators / 零エネルギーレゾナンス / ディラック作用素 / Lipschitz semigroup / generator / conservation law / stability / Hadamard well-posedness / abstract quasi-linear equation / wave front tracking solution / Riemann problem / Templ type / conservation laws / generation theorem / infinitesimal generators / semigroup of Lipschite operators / 無限小生成作用素 / 保存則系 / 安定性 / Hadamardの意味の適切性 / 抽象的準線形発展方程式 / covers of Riemann surfaces / Grothendieck Conjecture / absolute Galois group / braid group / mapping class group / Teichmueller space / outer Galois representation / anabelian geometry / グロタンデイーク予想 / グロタンディーク予想 / 絶対ガロア群 / 外ガロア表現 / 遠アーベル幾何 / scattering arnplitude / δ-like magnetic field / magnetic Scchrodinger operator / Aharonov-Bohm efrect / magnetic vortex / scattering amplitude / scattreing amplitude / point-like magneticfield / デルタ磁場 / Metric Invariants / Curvatures / Alexandrov spaces / 計量不変量 / アレキサンドロフ空間 / spectrum / P-Laplace operator / P-harmonic map / スペクトラム / 第1固有値 / P-ラプラシアン / P-harmonic morphism / グリーン核 / 無限グラフ / P-ラプラス作用素 / point interaction / scattering at low energy / magnetic Schrodinger operator / アハロノフ・ボウム効果 / デルタ型磁場 / レゾルベント収束 / scattering amplitudes / asymptotic distribution of eigenvalues / Schrodinger semigroup / exponential product formula / 非一様磁場 / 固有値分布 / レゾルベント / 固有値漸近分布 / シュレディンガー半群 / 指数積公式 / Laplacian for graphs / spectral zeta functions / spherical space forms / isospectral problem / Spin structure / グラフのラプラシアン / スペクトラルゼータ関数 / 球面空間形 / 等スペクトル問題 / スピン構造 / Dirac作用素 / Warped product / Comparison Theorem / Geodesic / Curvature / 捩れ積 / ねじれ積 / 双曲型 / 局所等質空間 / 作用 / 位相的性質 / 微分幾何学的量 / 多様体 / 等長変換群 / 等周不等式 / ホモトピー型 / A(p)構造 / 作用素 / 同境理論 / コホモロジー / リッチ曲率 / L関数 / ラプラシアン / 基本群 / Staeckel / Kaehler-Liouville / Hermite-Liouville様体 / Liouville多様体 / 半古典近似 / 最小跡 / 熱核 / 指数積近似 / 準古典漸近公式 / ソレノイド磁場 / 準古典近似 / 散乱位相 / 散乱全断面積 / アハラノフ・ポーム効果 / 準古典漸近解析 / スペクトル散乱理論 / 関数方程式の大域理論 / 双曲幾何学 / シュレーディンガー方程式 / 双曲計量 / 散乱行列 / S行列 / EIT / ディリクレ・ノイマン写像 / 逆問題 / ベリー関数 / モジュラー関数 / 定義体 / グロタンディーク・デッサン / 一般ホモロジー理論 / コンフィグレーション空間 / K理論 / 分類空間 / 同変ホモトピー論 / リ-マン幾何学 / 比較定理とその応用 / 幾何学不等式 / 位相構造 / 計量構造 Less
  • Research Projects

    (34 results)
  • Research Products

    (50 results)
  • Co-Researchers

    (61 People)
  •  Investigations of noncommutative Bloch theory and its geometric applicationsPrincipal Investigator

    • Principal Investigator
      勝田 篤
    • Project Period (FY)
      2024 – 2026
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11020:Geometry-related
    • Research Institution
      Keio University
  •  Density Theorems of Closed Geodesics for Nilpotent Extensions and Asymptotics of Heat KernelsPrincipal Investigator

    • Principal Investigator
      KATSUDA ATSUSHI
    • Project Period (FY)
      2018 – 2022
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11020:Geometry-related
    • Research Institution
      Kyushu University
  •  Structures of manifolds and asymptoticpropertiesPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2010 – 2012
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Kyushu University
  •  Development of various problems related to integrable geodesic flows

    • Principal Investigator
      KIYOHARA Kazuyoshi
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Geometric Structures and TopologyPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2007 – 2009
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Development of numerical computation brought by spectral theory and geometry

    • Principal Investigator
      ISOZAKI Hiroshi
    • Project Period (FY)
      2006 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      University of Tsukuba
  •  Asymptotic Analysis in Spectral and Scattering Theory

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      2006 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Global analysis
    • Research Institution
      Okayama University
  •  Problems related to integrable geodesic flows

    • Principal Investigator
      KIYOHARA Kazuyoshi
    • Project Period (FY)
      2006 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Metric invariants and space structures

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      2005 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University of Science
  •  モジュライ空間の算術幾何に対する種種のグラフ複合体の関与の研究

    • Principal Investigator
      NAKAMURA Hiroaki
    • Project Period (FY)
      2004 – 2005
    • Research Category
      Grant-in-Aid for Exploratory Research
    • Research Field
      Algebra
    • Research Institution
      Okayama University
  •  Relations of geometric structure of manifolds and graphs, spectre, asymptotic analysis and their applicationsPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Integrable geodesic flows and related problems

    • Principal Investigator
      KIYOHARA Kazuyoshi
    • Project Period (FY)
      2004 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Wellposedness of the Cauchy problems for hyperbolic systems with large data

    • Principal Investigator
      TANAKA Naoki
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Shizuoka University
      Okayama University
  •  studies on the relationship of the structure of manifolds and p-harmonic functions

    • Principal Investigator
      TAKEUCHI Hiroshi
    • Project Period (FY)
      2004 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Shikoku University
  •  Scattering of Dirac particles by mabnetic fields and spectral theory

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      2003 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Okayama University
  •  Galois groups and fundamental groups in anabelian geometry

    • Principal Investigator
      NAKAMURA Hiroaki
    • Project Period (FY)
      2002 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Spectra and Geometric structure of manifolds and graphPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Well-posedness and approximation of Cauchy problems for hyperbolic systems

    • Principal Investigator
      TANAKA Naoki
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Scattering by magnetic fields and Aharonov-Bohm effect

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      2001 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Relations between space-structures and curvatures

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      2000 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Geometric Structures on Manifolds and GraphsPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2000 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Spectral Theory for Schrodinger Operators with Magnetic Fields and its Application

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      1999 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (B).
    • Research Field
      Global analysis
    • Research Institution
      Okayama University
  •  The properties of P-harmonic maps and the application to Geometry

    • Principal Investigator
      TAKEUCHI Hiroshi
    • Project Period (FY)
      1999 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Shikoku University
  •  Geometric structure and topology of manifolds and graphsPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      1998 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  CURVATURE AND STRUCURE OF SPACES

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA 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
  •  Spectral and Scattering Theory and its Application

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Okayama University
      Ibaraki University
  •  計量構造と多様体構造

    • Principal Investigator
      酒井 隆
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  多様体の幾何構造と位相Principal Investigator

    • Principal Investigator
      勝田 篤
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  同変ホモトピー論とその応用

    • Principal Investigator
      SHIMAKAWA Kazuhisa
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  双曲力学系及び非線型偏微分方程式Principal Investigator

    • Principal Investigator
      勝田 篤
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for Encouragement of Young Scientists (A)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  計量構造と位相構造

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      1990
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Okayama University
  •  曲面論と多様体論の微分幾何学的研究

    • Principal Investigator
      森本 明彦
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Nagoya University
  •  一般コホモロジー論

    • Principal Investigator
      藤井 道一
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Okayama University

All 2022 2021 2020 2019 2013 2012 2011 2009 2007 2006 2005 2004

All Journal Article Presentation Book

  • [Book] Closed geodesics and heat kernels on nilpotent coverings2011

    • Author(s)
      A.Katsuda
    • Publisher
      Geometry and Something
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Journal Article] An extension of the Bloch-Floquet theory to the Heisenberg group and its applications to asymptotic problems for heat kernels and prime closed geodesics2022

    • Author(s)
      勝田 篤
    • Journal Title

      数理解析研究所講究禄

      Volume: 2201 Pages: 59-75

    • NAID

      120007170963

    • Open Access
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Journal Article] A rigidity theorem for Killing vector fields on compact manifolds with almost nonpositive Ricci curvature2021

    • Author(s)
      Katsuda, Atsushi; Nakamura, Takuya
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 149 Issue: 3 Pages: 1215-1224

    • DOI

      10.1090/proc/14742

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Journal Article] An Overview of Sunada's work up to age 602009

    • Author(s)
      Atsushi Katsuda
    • Journal Title

      Contemporary Mathematics 484

      Pages: 7-42

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] An overview of Sunada's work up to age 602009

    • Author(s)
      A. Katsuda, P.W. Sy
    • Journal Title

      Contemp. Math. 484

      Pages: 7-42

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Probl.Imaging 1・1

      Pages: 135-157

    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary representation and reconstruction of Riemannian Manifolds.2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging 1-1

      Pages: 135-157

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary distance and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Prob. Imaging 1

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] Stability of boundary representation and reconstruct ion of Riemannian Manifolds.2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging. 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Matti ; Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1 no. 1

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18340034
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2006

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging Vol 1, No 1

      Pages: 135-157

    • Data Source
      KAKENHI-PROJECT-18340034
  • [Journal Article] Boundary regularity for the Ricci equation, geometric convergence, and Gelfand's inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda 他(計5名)
    • Journal Title

      Invent.Math. 158

      Pages: 261-321

    • Data Source
      KAKENHI-PROJECT-16540069
  • [Journal Article] Boundary regularity for the Ricci equation, geometric convergence, and Gel' fand inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda 他3名
    • Journal Title

      Invent. Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Boundary regularity for the Ricci equat ion, geometric convergence, and Gel' fand inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda et al.
    • Journal Title

      Invent. Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Boundary regularity for Ricci equation,geometric convergence,and Gel'fand's inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda, et. al.
    • Journal Title

      Invent.Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-16540208
  • [Journal Article] Boundary regularity for the Ricci equation, geometric convergence, and Gel' fand inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda 他3名
    • Journal Title

      Invent.Math. 158

      Pages: 261-321

    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Boundary regularity for Ricci equation, geometori Convergence, and Gel'fand's inverse boundary problem2004

    • Author(s)
      M. Anderson, A. Katsuda, Y. Kurylev, M. Lassas, M. Taylor
    • Journal Title

      Invent. Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540208
  • [Presentation] Nash の埋め込み定理の原証明とその応用可能性2022

    • Author(s)
      勝田 篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] Riemann の教授資格取得講演と現代のリーマン幾何学2022

    • Author(s)
      勝田 篤
    • Organizer
      研究会「直観幾何学 2022」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] 素数と素閉測地線ーDirichlet,Riemann,Selbergー2022

    • Author(s)
      勝田 篤
    • Organizer
      研究会「直観幾何学 2022」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] An extension of the Bloch-Floquet theory to the Heisenberg group and its applications to geometric Chebotarev density theorems andlong time asymptotics of the heat kernels2022

    • Author(s)
      勝田 篤
    • Organizer
      福岡大学 微分幾何研究集会
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] 閉測地線, 熱核, ハイゼンベルグ群2020

    • Author(s)
      勝田 篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] Closed geodesics and heat kernels for Heisenberg extensions2019

    • Author(s)
      勝田 篤
    • Organizer
      研究集会「 多様体上の微分方程式 」金沢シリーズ第18回
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] Toward a geometric density theorem for nilpotent extensions2013

    • Author(s)
      A. Katsuda
    • Organizer
      Low dimensional topology and number theory V
    • Place of Presentation
      福岡ソフトリサーチパーク
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] ハイゼンベルグ群に対する幾何学的密度定理に向けて2013

    • Author(s)
      勝田 篤
    • Organizer
      小研究会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Toward a geometric dennsity theorem for nilpotent extensions2013

    • Author(s)
      Atsushi Katsuda
    • Organizer
      Low dimennsional topology and number theory V
    • Place of Presentation
      Fukuoka,
    • Invited
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] ハイゼンベルグ群に対する幾何学的密度定理に向けて2013

    • Author(s)
      勝田 篤
    • Organizer
      研究集会 測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Closed geodesics and heat kernels on nilpotent coverings2012

    • Author(s)
      勝田 篤
    • Organizer
      研究集会 測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Closed geodesics and heat kernels on nilpotent coverings2012

    • Author(s)
      勝田篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学(招待講演)
    • Year and Date
      2012-01-09
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] 境界付多様体の境界距離表現と内部距離2011

    • Author(s)
      勝田 篤
    • Organizer
      研究集会 測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Density theorems of closed geodesics for nilpotent extensions2011

    • Author(s)
      勝田篤
    • Organizer
      Geometry and Something
    • Place of Presentation
      福岡大学(招待講演)
    • Year and Date
      2011-11-03
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] 境界付多様体の境界距離表現と内部距離2011

    • Author(s)
      勝田篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学(熊本)
    • Year and Date
      2011-01-08
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Density theorems of closed geodesics for nilpotent extensions2011

    • Author(s)
      勝田 篤
    • Organizer
      福岡大学微分幾何学研究会
    • Place of Presentation
      福岡大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis in Geometry and Number Theory
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-08-07
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis in Geometry and Number Theory
    • Place of Presentation
      Nagoya Univ
    • Year and Date
      2007-08-07
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Spectral analysis in geometry2007

    • Author(s)
      勝田篤
    • Organizer
      岡山幾何学談話会
    • Place of Presentation
      岡山大学
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      勝田 篤
    • Organizer
      Spectral Analysis in Geometry and Number theory
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-08-07
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Spectral Analysis in Geometry2007

    • Author(s)
      A. Katsuda
    • Organizer
      Okayama Colloquium on Geometry
    • Place of Presentation
      Okayama Univ
    • Year and Date
      2007-07-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Spectral Analysis in Geometry2007

    • Author(s)
      勝田 篤
    • Organizer
      第17回岡山幾何学談話会
    • Place of Presentation
      岡山大学
    • Year and Date
      2007-07-27
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      勝田篤
    • Organizer
      International Symposium“Spectral Analysis in Geometry and Number Theory"
    • Place of Presentation
      名古屋大学
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis, Global Analysis and PDE 2005
    • Place of Presentation
      Keio Univ
    • Year and Date
      2005-05-13
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] On the stability of the Gel'fand inverse spectral problem2005

    • Author(s)
      勝田 篤
    • Organizer
      Spectral Analysis, Global Analysis and PDE 2005
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2005-05-13
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Gel'fandのスペクトル逆問題の安定性について2005

    • Author(s)
      勝田 篤
    • Organizer
      日本数学会年会幾何学分科会特別講演
    • Place of Presentation
      日本大学
    • Year and Date
      2005-03-30
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Tohoku Geometry Seminar
    • Place of Presentation
      Tohoku Univ
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Gel'fandのスペクトル逆問題の安定性について2005

    • Author(s)
      勝田 篤
    • Organizer
      東北大学幾何セミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Special lecture at annual meeting of Math. Soc. Japan
    • Place of Presentation
      Nihon Univ
    • Year and Date
      2005-03-30
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
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  • 2.  TAMURA Hideo (30022734)
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  • 3.  SHIMAKAWA Kazuhisa (70109081)
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