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Geometric property of the Gaussian estimate of the gradient of the heat kernel

Research Project

Project/Area Number 18740084
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

ISHIWATA Satoshi  University of Tsukuba, 大学院・数理物質科学研究科, 助教 (70375393)

Research Collaborator THIERRY Coulhon  Cergy-Pontoise大学(フランス), 教授
KOTANI Motoko  東北大学, 大学院・理学研究科, 教授 (50230024)
KUMAGAI Takashi  京都大学, 大学院・理学研究科, 教授 (90234509)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords多様体上の解析学 / 熱核の長時間挙動 / 熱核のgradient評価 / Sobolevの不等式 / Poincare不等式 / 熱核の長時間挙 / 連結和 / gluing / 中心極限定理 / 熱核のgradient estimate / 熱核のガウス型評価 / ベキ零離散群の連結性 / Poincareの不等式
Research Abstract

非コンパクトリーマン多様体及び無限グラフにおいて,近年熱核の長時間挙動と空間の大域的な性質との深いつながりが明らかとなってきた.このような状況のもと,本研究では熱核の空間方向へのgradient について研究を行い,
(1)熱核のgradient のGauss 型評価がグラフのある摂動のもとでは安定であること,
(2) Dungey の方法によりベキ零群の作用のあるグラフ上では熱核のgradient がGauss 型評価を持つこと,
(3)ベキ零被覆グラフの中心極限定理がグラフのある摂動のもとで安定であること,
(4)正方格子グラフの連結和の下で熱核のgradient のGauss 型評価が成り立たないための十分条件,を得た.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (36 results)

All 2009 2008 2007 2006 Other

All Journal Article (5 results) (of which Peer Reviewed: 4 results) Presentation (29 results) Remarks (2 results)

  • [Journal Article] A central limit theorem on modified graphs of nilpotent covering graphs.2009

    • Author(s)
      S. Ishiwata
    • Journal Title

      Spectral Analysis in Geomety and Number Theory, Contemporary Mathematics American Mathematical Sociery 484

      Pages: 59-72

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gradient estimate of the heat kernel on modified graphs.2007

    • Author(s)
      S. Ishiwata
    • Journal Title

      Potential Analysis 27 no.4

      Pages: 335-351

    • NAID

      120007139116

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discrete version of Dungey's proof for the gradient heat kernel estimate on coverings.2007

    • Author(s)
      S. Ishiwata
    • Journal Title

      Annales Mathematiques Blaise Pascal 14, no.1

      Pages: 93-102

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gradient estimate of the heat kernel on modified graphs2007

    • Author(s)
      Satoshi Ishiwata
    • Journal Title

      Potential Analysis 27 no.4

      Pages: 335-351

    • NAID

      120007139116

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Discrete version of Dungey's proof for the gradient heat kernel estimate on coverings2007

    • Author(s)
      Satoshi Ishiwata
    • Journal Title

      Annales Mathematiques Blaise Pascal 14・1

      Pages: 93-102

    • Related Report
      2006 Annual Research Report
  • [Presentation] Heat kernel on gluings2009

    • Author(s)
      石渡聡
    • Organizer
      数理情報科学セミナー
    • Place of Presentation
      広島大学総合科学部
    • Year and Date
      2009-01-26
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Heat kernel on gluings2008

    • Author(s)
      石渡聡
    • Organizer
      微分トポロジーセミナー
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2008-12-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Hear kernel on gluings2008

    • Author(s)
      石渡聡
    • Organizer
      微分トポロジーセミナー
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2008-12-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] Heat kernel on gluings2008

    • Author(s)
      石渡聡
    • Organizer
      松江セミナー
    • Place of Presentation
      島根大学総合理工学部
    • Year and Date
      2008-11-05
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] 「Gradient heat kernel estimate on gluings2008

    • Author(s)
      石渡聡
    • Organizer
      Stochastic Analysis and Applications, 2008
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2008-09-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2008

    • Author(s)
      石渡聡
    • Organizer
      Stcichastic Analysis and Applications, 2008
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2008-09-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] Heat kernel on gluings2008

    • 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
      2008-02-18
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Heat kernel on gluings2008

    • Author(s)
      石渡聡
    • 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
      2008-01-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Heat kernel on gluings2008

    • Author(s)
      石渡聡
    • Organizer
      福岡大学微分幾何研究会
    • Place of Presentation
      福岡大学
    • Year and Date
      2008-01-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] 「熱核のgradient評価とRiesz変換のL^p有界性2007

    • Author(s)
      石渡聡
    • Organizer
      バナッハ環セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2007-11-21
    • Related Report
      2008 Final Research Report
  • [Presentation] ベキ零離散群上のランダム・ウォークの漸近挙動について2007

    • Author(s)
      石渡聡
    • Organizer
      仙台放物型・楕円型方程式研究集会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-11-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Behavior of the Heat kernel on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      談話会
    • Place of Presentation
      東京理科大学理工学部
    • Year and Date
      2007-11-08
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      微分幾何学火曜セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2007-10-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      」確率論と幾何学
    • Place of Presentation
      熊本大学
    • Year and Date
      2007-10-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      確率論と幾何学
    • Place of Presentation
      熊本大学教育学部
    • Year and Date
      2007-10-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村阿蘇
    • Year and Date
      2007-09-03
    • Related Report
      2008 Final Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      幾何学阿蘇研究集会
    • Place of Presentation
      休暇村南阿蘇
    • Year and Date
      2007-09-03
    • Related Report
      2007 Annual Research Report
  • [Presentation] Random walks on nilpotent covering graphs2007

    • Author(s)
      石渡聡
    • Organizer
      International Conference "Spectral Analysis in Geometry and Number Theory" on the occasion of Toshikazu Sunada's 60th birthday
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-08-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Gradient heat kernel estimate on gluings2007

    • Author(s)
      石渡聡
    • Organizer
      談話会
    • Place of Presentation
      岡山大学理学部
    • Year and Date
      2007-07-04
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Connectivity on discrete nilpotent groups2007

    • Author(s)
      石渡聡
    • Organizer
      Analysis on Graphs and Fractals
    • Place of Presentation
      Cardiff University, UK
    • Year and Date
      2007-05-31
    • Related Report
      2008 Final Research Report
  • [Presentation] ベキ零離散群の連結性2007

    • Author(s)
      石渡聡
    • Organizer
      2007年度年会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-29
    • Related Report
      2008 Final Research Report
  • [Presentation] グラフ上のランダム・ウォークに関する関数解析的中心極限定理2007

    • Author(s)
      石渡聡
    • Organizer
      神奈川大学数学教室談話会
    • Year and Date
      2007-01-26
    • Related Report
      2008 Final Research Report
  • [Presentation] ベキ零離散群の連結性2006

    • Author(s)
      石渡聡
    • Organizer
      多様体上の微分方程式
    • Place of Presentation
      金沢大学
    • Year and Date
      2006-12-06
    • Related Report
      2008 Final Research Report
  • [Presentation] Connectivity of discrete nilpotent groups2006

    • Author(s)
      石渡聡
    • Organizer
      Sendai Max Dehn seminar
    • Place of Presentation
      東北大学
    • Year and Date
      2006-10-20
    • Related Report
      2008 Final Research Report
  • [Presentation] A connectivity of discrete nilpotent groups2006

    • Author(s)
      石渡聡
    • Organizer
      Department Lecture, University of Cyprus
    • Place of Presentation
      キプロス
    • Year and Date
      2006-10-04
    • Related Report
      2008 Final Research Report
  • [Presentation] ベキ零離散群の連結性2006

    • Author(s)
      石渡聡
    • 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
      2006-09-12
    • Related Report
      2008 Final Research Report
  • [Presentation] 熱核のgradientがガウス型評価を持つ空間と持たない空間2006

    • Author(s)
      石渡聡
    • Organizer
      第53回幾何学シンポジウム
    • Place of Presentation
      金沢大学
    • Year and Date
      2006-08-07
    • Related Report
      2008 Final Research Report
  • [Presentation] A stability of a gradient estimate for the heat kernel on graphs2006

    • Author(s)
      石渡聡
    • Organizer
      Asymptotics in Geometry
    • Place of Presentation
      東北大学
    • Year and Date
      2006-07-15
    • Related Report
      2008 Final Research Report
  • [Presentation] 熱核のgradientのガウス型評価2006

    • Author(s)
      石渡聡
    • Organizer
      東京確率論セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2006-06-16
    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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