Takahashi Junya 高橋淳也

… Alternative Names

TAKAHASHI Junnya 高橋淳也

高橋淳也タカハシジュンヤ

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Researcher Number	10361156
Other IDs
Affiliation (Current)	2025: 東北大学, 情報科学研究科, 助教
Affiliation (based on the past Project Information) *help	2012 – 2022: 東北大学, 情報科学研究科, 助教 2009: 東北大学, 情報科学研究科, 助教 2007: Tohoku University, 大学院・情報科学研究科, 助教 2007: 東北大学, 情報科学研究科, 助教 2004 – 2006: 東北大学, 大学院・情報科学研究科, 助手
Review Section/Research Field	Principal Investigator Geometry Except Principal Investigator Basic analysis / Geometry
Keywords	Principal Investigator 微分形式 / 固有値 / ラプラシアン / 小さい固有値 / 幾何学 / 特異点 / リーマン多様体の崩壊 / 固有値の収束 / Riemann多様体の崩壊 / Laplacian … More / スペクトル / 自己共役性 / エッジ特異点 / 消滅定理 / L^2 ストークス定理 / L^2 調和形式 / ホッジ理論 / ベッチ数 / リーマン沈め込み / 非負断面曲率 / 球面 / 体積一定 / 断面曲率 / L2 調和形式 / L2 ストークス定理 / リーマン計量の変形 / ラフ・ラプラシアン / ホッジ・ラプラシアン / 大きい固有値 / ノルムの集中 / 多様体の崩壊 / 交叉コホモロジー群 / スペクトル幾何学 / 調和形式 / リーマン多様体 / コホモロジー群 / 崩壊 / Riemann多様体 / 極限 / 収束 / L^2-解析 / 固有関数 … More Except Principal Investigator レヴナー方程式 / ベルトラミ方程式 / シストール / 双曲距離 / ラプラシアン / タイヒミュラー型定理 / 双曲幾何 / モジュラス距離 / モジュラー方程式 / 係数問題 / 擬等角写像 / 調和写像 / リーマン面 / 楕円型作用素 / 非線形レゾルベント / 一様完全 / 擬等角拡張 / 単葉調和函数 / スペクトル / タイヒミュラーの定理 / 平面領域 / モジュラス / 双曲計量 / P-エネルギー / p-エネルギー / 2―調和写像 / 2-調和写像 / リーマン多様体 / 有効抵抗 / ネットワーク / Gromov-Hausdorff収束 / 変分収束 / エネルギー形式 / 測度距離空間 Less

Analysis of elliptic operators and its applications to Geometric Function Theory
- Principal Investigator
  
  Sugawa Toshiyuki
- Project Period (FY)
  2017 – 2021
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Basic analysis
- Research Institution
  Tohoku University
Studies of geometry of singularities and the eigenvalues of the Hodge-LaplacianPrincipal Investigator
- Principal Investigator
  
  Takahashi Junya
- Project Period (FY)
  2016 – 2021
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Geometry
- Research Institution
  Tohoku University
Studies on the limit of the eigenvalues of the Hodge-Laplacian under collapsing of Riemannian manifoldsPrincipal Investigator
- Principal Investigator
  
  Takahashi Junya
- Project Period (FY)
  2012 – 2015
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- 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
微分形式における小さい固有値の位相的性質の研究Principal Investigator
- Principal Investigator
  
  高橋淳也
- Project Period (FY)
  2007
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Tohoku University
リーマン多様体の崩壊と微分形式のラプラシアンの固有値の研究Principal Investigator
- Principal Investigator
  
  高橋淳也
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Tohoku University

All 2022 2018 2016 2015 2012 2006 2005 Other

All Journal Article Presentation

[Journal Article] Small eigenvalues of the rough and Hodge Laplacians under fixed volume2022
- Author(s)
  Colette Ann'e and Junya Takahashi
- Journal Title
  
  Annales de la Facult'e des Sciences de Toulouse
  
  Volume: -
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-16K05117
[Journal Article] $L^2$-harmonic forms on incomplete Riemannian manifolds with positive Ricci curvature2018
- Author(s)
  Junya Takahashi
- Journal Title
  
  Mathematics, Special Issue, Differential Geometry
  
  Volume: 印刷中
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-16K05117
[Journal Article] L^2-harmonic forms on incomplete Riemannian manifolds with positive Ricci curvature2018
- Author(s)
  Junya Takahashi
- Journal Title
  
  Mathematics
  
  Volume: 6 Issue: 5 Pages: 1-11
- DOI
  10.3390/math6050075
- Peer Reviewed / Open Access
- Data Source
  KAKENHI-PROJECT-16K05117, KAKENHI-PROJECT-17H02847
[Journal Article] Partial collapsing and the spectrum of the Hodge-de Rham operator2015
- Author(s)
  Colette Ann'e and Junya Takahashi
- Journal Title
  
  Analysis & PDE
  
  Volume: 8 Issue: 5 Pages: 1025-1050
- DOI
  10.2140/apde.2015.8.1025
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-24740034
[Journal Article] p-spectrum and collapsing of connected sums2012
- Author(s)
  Colette Ann'e and Junya Takahashi
- Journal Title
  
  Transactions of the American Mathematical Society
  
  Volume: 364 Issue: 4 Pages: 1711-1735
- DOI
  10.1090/s0002-9947-2011-05351-1
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-24740034
[Journal Article] Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian2006
- Author(s)
  Junya Takahashi
- Journal Title
  
  Manuscripta Mathematica 121
  
  Pages: 191-200
- Data Source
  KAKENHI-PROJECT-16740026
[Journal Article] Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms2005
- Author(s)
  Junya Takahashi
- Journal Title
  
  Mathematische Zeitschrift 250
  
  Pages: 43-57
- Data Source
  KAKENHI-PROJECT-16740026
[Journal Article] The gap of the eigenvalues for $p$-forms and harmonic $p$-forms of constant length2005
- Author(s)
  Junya Takahashi
- Journal Title
  
  Journal of Geometry and Physics 54
  
  Pages: 476-484
- Data Source
  KAKENHI-PROJECT-16740026
[Journal Article] Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms2005
- Author(s)
  Junya Takahashi
- Journal Title
  
  Mathematische Zeitschrift (発表予定)
- Data Source
  KAKENHI-PROJECT-16740026
[Journal Article] The gap of the eigenvalues for $p$-forms and harmonic $p$-forms constant length2005
- Author(s)
  Junya Takahashi
- Journal Title
  
  Journal of Geometry and Physics (発表予定)
- Data Source
  KAKENHI-PROJECT-16740026
[Presentation] 体積一定下での Hodge-Laplacian と rough Laplacian の小さい固有値2022
- Author(s)
  高橋淳也, Colette Ann'e
- Organizer
  日本数学会幾何学分科会
- Data Source
  KAKENHI-PROJECT-16K05117
[Presentation] Partial collapsing and the spectrum of the Hodge-Laplacian2016
- Author(s)
  高橋淳也
- 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（石川県金沢市）
- Year and Date
  2016-11-19
- Invited
- Data Source
  KAKENHI-PROJECT-16K05117
[Presentation] Partial collapsing and the spectrum of the Hodge-Laplacian
- Author(s)
  高橋淳也
- Organizer
  幾何セミナー
- Place of Presentation
  東北大学理学部
- Invited
- Data Source
  KAKENHI-PROJECT-24740034
[Presentation] Partial collapsing and the spectrum of the Hodge-de Rham operator
- Author(s)
  高橋淳也
- Organizer
  Geometry and Probability
- Place of Presentation
  京都大学理学部
- Invited
- Data Source
  KAKENHI-PROJECT-24740034
[Presentation] 一般化された連結和の崩壊と Hodge-Laplacian の固有値の収束
- Author(s)
  高橋淳也
- Organizer
  第60回幾何学シンポジウム
- Place of Presentation
  東京工業大学
- Invited
- Data Source
  KAKENHI-PROJECT-24740034
[Presentation] Partial collapsing and the spectrum of the Hodge-Laplacian
- Author(s)
  高橋淳也
- Organizer
  リーマン幾何と幾何解析
- Place of Presentation
  筑波大学
- Invited
- Data Source
  KAKENHI-PROJECT-24740034

1. NAYATANI Shin (70222180)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
2. KATO Shin (10243354)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
3. KUMURA Hironori (30283336)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
4. KASUE Atsushi (40152657)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
5. URAKAWA Hajime (50022679)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
6. Sugawa Toshiyuki (30235858)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
7. 志賀啓成 (10154189)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
8. 相川弘明 (20137889)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
9. 柳原宏 (30200538)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
10. 船野敬 (40614144)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
11. 坂口茂 (50215620)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
12. 松崎克彦 (80222298)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. 菊田伸 (40736790)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. 金城絵利那 (40746559)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

Takahashi Junya 高橋 淳也

TAKAHASHI Junnya 高橋 淳也

高橋 淳也 タカハシ ジュンヤ

Research Projects

Research Products

Co-Researchers

Analysis of elliptic operators and its applications to Geometric Function Theory

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Studies of geometry of singularities and the eigenvalues of the Hodge-LaplacianPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Studies on the limit of the eigenvalues of the Hodge-Laplacian under collapsing of Riemannian manifoldsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Convergence theory of metric measure spaces and its development

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

微分形式における小さい固有値の位相的性質の研究Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

リーマン多様体の崩壊と微分形式のラプラシアンの固有値の研究Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Small eigenvalues of the rough and Hodge Laplacians under fixed volume2022

Author(s)

Journal Title

Data Source

[Journal Article] $L^2$-harmonic forms on incomplete Riemannian manifolds with positive Ricci curvature2018

Author(s)

Journal Title

Data Source

[Journal Article] L^2-harmonic forms on incomplete Riemannian manifolds with positive Ricci curvature2018

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Partial collapsing and the spectrum of the Hodge-de Rham operator2015

Author(s)

Journal Title

DOI

Data Source

[Journal Article] p-spectrum and collapsing of connected sums2012

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Collapsing to Riemannian manifolds with boundary and the convergence of the eigenvalues of the Laplacian2006

Author(s)

Journal Title

Data Source

[Journal Article] Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms2005

Author(s)

Journal Title

Data Source

[Journal Article] The gap of the eigenvalues for $p$-forms and harmonic $p$-forms of constant length2005

Author(s)

Journal Title

Data Source

[Journal Article] Vanishing of cohomology groups and large eigenvalues of the Laplacian on $p$-forms2005

Author(s)

Journal Title

Takahashi Junya 高橋淳也

TAKAHASHI Junnya 高橋淳也

高橋淳也タカハシジュンヤ