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Geometric properties on the threshold of the Sobolev type inequalities and generalization to metric spaces

Research Project

Project/Area Number 21740034
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionYamagata University (2012)
University of Tsukuba (2009-2011)

Principal Investigator

ISHIWATA Satoshi  山形大学, 理学部, 准教授 (70375393)

Research Collaborator KOTANI Motoko  東北大学, 大学院・理学研究科, 教授 (50230024)
KUMAGAI Takashi  京都大学, 理学部, 教授 (90234509)
OHTA Shin-ichi  京都大学, 理学部, 准教授 (00372558)
ALEXANDER Grigoryan  ドイツ Bielefeld大学, 教授
THIERRY Coulhon  オーストラリアAustralian National University, 教授
Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords熱核の長時間挙動 / Poincare不等式 / Sobolev不等式 / 連結和 / 熱核 / hitting probability / 等周不等式 / bottleneck effect / Poincareの不等式 / Sobolevの不等式
Research Abstract

On non-compact Riemannian manifolds and infinite graphs, therelationship among global geometric structure, geometric inequalities and long time heatkernel behavior is well investigated by many researchers. In this research, we considerconnected sums and we obtain a precise relationship between a structure of bottlenecknessand isoperimetric inequality, Poincare inequality and long time heat kernel behavior.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (38 results)

All 2012 2011 2010 2009 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (35 results) (of which Invited: 3 results) Remarks (1 results)

  • [Journal Article] Heat kernel estimates on a connected sum of two copies of R^n along a surface of revolution2012

    • Author(s)
      A. Grigoryan, S. Ishiwata
    • Journal Title

      Global and Stochastic Analysis

      Volume: 2 Pages: 29-65

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates on a connected sum of two copies of R^n along a surface of revolution2012

    • Author(s)
      Satoshi Ishiwata
    • Journal Title

      Global and Stochastic Analysis

      Volume: 2 Pages: 29065-29065

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Heatkernel estimates on connected sums with non-compactjoint2012

    • Organizer
      WeeklySeminar
    • Place of Presentation
      香港中文大学
    • Year and Date
      2012-03-26
    • Related Report
      2012 Final Research Report
  • [Presentation] Heat kernel estimates on connected sums with non-compact joint2012

    • Author(s)
      石渡聡
    • Organizer
      Weekly Seminar
    • Place of Presentation
      香港中文大学(中国)(招待講演)
    • Year and Date
      2012-03-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Heatkernel estimates on connected sums with non-compactjoint2012

    • Organizer
      CornellAnalysis Seminar
    • Place of Presentation
      Cornell大学
    • Year and Date
      2012-01-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Heat kernel estimates on connected sums with non-compact joint2012

    • Author(s)
      石渡聡
    • Organizer
      Cornell Analysis Seminar
    • Place of Presentation
      Cornell大学(米国)(招待講演)
    • Year and Date
      2012-01-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] 非コンパクトな連結部分を持つ連結和上の熱核評価2012

    • Author(s)
      石渡 聡
    • Organizer
      東北大学幾何学セミナー
    • Place of Presentation
      東北大学理学部
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 連結和上の熱核評価2012

    • Author(s)
      石渡 聡
    • 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
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Heat kernel estimates on a connected sum along a joing with a capacity groth2012

    • Author(s)
      石渡 聡
    • Organizer
      Advances on Fractals and Related Topics
    • Place of Presentation
      香港中文大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Heat kernel estimates onnon-compact gluings2011

    • Organizer
      Long Term Workshop Geometry and Analysis
    • Place of Presentation
      京都大学
    • Year and Date
      2011-03-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Heat kernel estimates on non-compact gluings2011

    • Author(s)
      石渡聡
    • Organizer
      Long Term Workshop-Geometry and Analysis
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2011-03-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Heat kernel estimates onnon-compact gluings2011

    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-02-19
    • Related Report
      2012 Final Research Report
  • [Presentation] Heat kernel estimates on non-compact gluings2011

    • Author(s)
      石渡聡
    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-02-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] 熱核のボトルネック型評価と第1ノイマン固有値2010

    • Organizer
      東工大数理解析セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2010-10-29
    • Related Report
      2012 Final Research Report
  • [Presentation] 熱核のボトルネック型評価と第1ノイマン固有値2010

    • Author(s)
      石渡聡
    • Organizer
      東工大数理解析セミナー
    • Place of Presentation
      東京工業大学(招待講演)
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Heat kernel estimates onnon-compact gluings2010

    • Organizer
      京都大学微分トポロジーセミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2010-10-22
    • Related Report
      2012 Final Research Report
  • [Presentation] Heat kernel estimates on non-compact gluings2010

    • Author(s)
      石渡聡
    • Organizer
      京都大学微分トポロジーセミナー
    • Place of Presentation
      京都大学(招待講演)
    • Year and Date
      2010-10-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] 熱核のボトルネック型評価と第1ノイマン固有値2010

    • Organizer
      第9回 RDSセミナー
    • Place of Presentation
      明治大学
    • Year and Date
      2010-10-18
    • Related Report
      2012 Final Research Report
  • [Presentation] 熱核のボトルネック型評価と第1ノイマン固有値2010

    • Author(s)
      石渡聡
    • Organizer
      第9回RDSセミナー
    • Place of Presentation
      明治大学(招待講演)
    • Year and Date
      2010-10-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] 熱核のボトルネック型評価と第1ノイマン固有値2010

    • Organizer
      筑波大学解析セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-10-13
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] Heat kernel estimates on non-compactgluings2010

    • Organizer
      Research seminarGeometric Analysis
    • Place of Presentation
      Bielefeld大学
    • Year and Date
      2010-07-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Heat kernel estimates on non-compact gluings2010

    • Author(s)
      石渡聡
    • Organizer
      Research seminar Geometric Analysis
    • Place of Presentation
      Bielefeld大学 ドイツ連邦共和国(招待講演)
    • Year and Date
      2010-07-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Heat kernel on non-compact gluings2010

    • Organizer
      筑波大学微分幾何学火曜セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-05-11
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] ボトルネック型熱核評価を持つ多様体の幾何学的特徴付け2010

    • Organizer
      日本数学会2010年度年会
    • Year and Date
      2010-03-25
    • Related Report
      2012 Final Research Report
  • [Presentation] ボトルネック型熱核評価を持つ多様体の幾何学的特徴付け2010

    • Author(s)
      石渡聡
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Manifolds with abottlenecktype heatkernel estimate2010

    • Organizer
      Manifolds with abottlenecktype heatkernel estimate
    • Place of Presentation
      香港中文大学
    • Year and Date
      2010-03-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Manifolds with a bottleneck type heat kernel estimate2010

    • Author(s)
      石渡聡
    • Organizer
      Analysis and Geometry of Fractals and Metric Measure spaces
    • Place of Presentation
      香港中文大学、中国
    • Year and Date
      2010-03-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] ボトルネック型熱核評価を持つ多様体の幾何学的特徴付け2010

    • Organizer
      金沢大学数理科学談話会
    • Year and Date
      2010-02-10
    • Related Report
      2012 Final Research Report
  • [Presentation] ボトルネック型熱核評価を持つ多様体の幾何学的特徴付け2010

    • Author(s)
      石渡聡
    • Organizer
      数理学談話会
    • Place of Presentation
      金沢大学
    • Year and Date
      2010-02-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] ボトルネック型熱核評価を持つ多様体の幾何学的特徴付け2010

    • Organizer
      確率論と幾何学
    • Place of Presentation
      京都大学
    • Year and Date
      2010-01-09
    • Related Report
      2012 Final Research Report 2009 Annual Research Report
  • [Presentation] ボトルネック型熱核評価を持つ多様体の幾何学的特徴付け2009

    • Organizer
      確率論シンポジウム
    • Place of Presentation
      愛媛大学
    • Year and Date
      2009-12-17
    • Related Report
      2012 Final Research Report 2009 Annual Research Report
  • [Presentation] Smallness of the first Neumann eigenvalues under a bottleneck heat kernelestimate2009

    • Organizer
      Research seminar "Geometric Analysis"
    • Place of Presentation
      Bielefeld大学
    • Year and Date
      2009-09-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Smallness of the first Neumann eigenvalues under a bottleneck heat kernel estimate2009

    • Author(s)
      石渡聡
    • Organizer
      Research seminar "Geometric Analysis"
    • Place of Presentation
      Bielefeld 大学ドイツ
    • Year and Date
      2009-09-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] Gradient heat kernel estimate ongluings2009

    • Organizer
      33rd Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      Berlin工科大学
    • Year and Date
      2009-07-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2009

    • Author(s)
      石渡聡
    • Organizer
      33rd Conference on Stochastic Processes and Their Applications
    • Place of Presentation
      Berlin 工科大学 ドイツ
    • Year and Date
      2009-07-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] The gradient heat kernel estimate ongluing2009

    • Organizer
      Research seminar "GeometricAnalysis"
    • Place of Presentation
      Bielefeld大学
    • Year and Date
      2009-05-07
    • Related Report
      2012 Final Research Report
  • [Presentation] The gradient heat kernel estimate on gluings2009

    • Author(s)
      石渡聡
    • Organizer
      Research seminar "Geometric Analysis"
    • Place of Presentation
      Bielefeld 大学 ドイツ
    • Year and Date
      2009-05-07
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.tsukuba.ac.jp/~ishiwata/research/research.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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