• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Geometric analysis for non-symmetric generators on Riemannian manifolds

Research Project

Project/Area Number 17K05215
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionYamagata University

Principal Investigator

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

Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords熱核 / ポアンカレ定数 / 連結和 / 非対称ランダム・ウォーク / べき零被覆グラフ / 中心極限定理 / 非対称ランダムウォーク / ポアンカレ不等式
Outline of Final Research Achievements

In this research project, we investigate geoemtric analysis on a connected sum of non-compact Riemannian manifolds. In particular, we obtain optimal estimates of the long time behavior of the heat kernel and the Poincare constant on manifold with ends. Almostly, the project was done as a joint work with Professor Alexander Grigor'yan from Bielefeld University in Germany and Professor Laurent Saloff-Coste from Cornell University in the US.

Academic Significance and Societal Importance of the Research Achievements

従来、トポロジーなどで使われていた空間の連結和という操作は幾何解析学とは相性が悪く、研究が進んでいなかった。本研究ではこの連結和という解析的には扱いにくい対象上の解析にチャレンジし、適切な仮定のもと、最良の結果を得た。この結果により、例えば結節点のあるような物体の中をランダムに動く粒子や信号がどちらに動きやすいか?という問題についての論理的な根拠を与え、従来よりも効率のよいシステムの開発に貢献することができる。

Report

(7 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (28 results)

All 2023 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (12 results) Journal Article (7 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 7 results,  Open Access: 1 results) Presentation (9 results) (of which Int'l Joint Research: 5 results,  Invited: 9 results)

  • [Int'l Joint Research] Universitat Bielefeld(ドイツ)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Cornell University(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] University of Bielefeld(ドイツ)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Cornell University(米国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Bielefeld University(ドイツ)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Cornell University(米国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Bielefeld University(ドイツ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Cornell University(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Universitat Bielefeld(ドイツ)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Cornell University(米国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Universitat Bielefeld(Germany)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Cornell University(米国)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Poincar? constant on manifolds with ends2023

    • Author(s)
      Grigor'yan Alexander、Ishiwata Satoshi、Saloff‐Coste Laurent
    • Journal Title

      Proceedings of the London Mathematical Society

      Volume: - Issue: 6 Pages: 1961-2012

    • DOI

      10.1112/plms.12522

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Geometric analysis on manifolds with ends2021

    • Author(s)
      Alexander Grigor’yan,Satoshi Ishiwata, and Laurent Saloff-Coste
    • Journal Title

      Advances in Analysis and Geometry

      Volume: 3 Pages: 325-344

    • DOI

      10.1515/9783110700763-011

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Central limit theorems for non-symmetric random walks on nilpotent covering graphs: Part I2020

    • Author(s)
      Ishiwata Satoshi、Kawabi Hiroshi、Namba Ryuya
    • Journal Title

      Electronic Journal of Probability

      Volume: 25 Issue: none Pages: 1-46

    • DOI

      10.1214/20-ejp486

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Central Limit Theorems for Non-Symmetric Random Walks on Nilpotent Covering Graphs: Part II2020

    • Author(s)
      Ishiwata Satoshi、Kawabi Hiroshi、Namba Ryuya
    • Journal Title

      Potential Analysis

      Volume: online Issue: 1 Pages: 1-40

    • DOI

      10.1007/s11118-020-09851-7

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] 非コンパクトリーマン多様体上の熱核評価 - 最近の発展 -2018

    • Author(s)
      石渡聡
    • Journal Title

      数学

      Volume: 71 Pages: 77-92

    • NAID

      130007975509

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Heat kernel estimates on connected sums of parabolic manifolds2018

    • Author(s)
      Alexander Grigor'yan, Satoshi Ishiwata, L. Saloff-Coste
    • Journal Title

      Journal de Mathematiques Pures et Appliquees

      Volume: 113 Pages: 155-194

    • DOI

      10.1016/j.matpur.2018.03.002

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Can one observe the bottleneckness of a space by the heat distribution?2017

    • Author(s)
      Satoshi Ishiwata
    • Journal Title

      Mathematical Physics and Computer Simulation, Volgograd State University

      Volume: 20 Pages: 77-88

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] Poincar´e constant on manifolds with ends2023

    • Author(s)
      Satoshi Ishiwata
    • Organizer
      Open Japanese-German conference on stochastic analysis and applications
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多様体の離散近似2022

    • Author(s)
      石渡聡
    • Organizer
      オンライン勉強会:機械学習の数理
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Heat kernel estimates on connected sums of parabolic manifolds2022

    • Author(s)
      石渡聡
    • Organizer
      Hokkaido University online seminar
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Geometric analysis on manifolds with ends2021

    • Author(s)
      Satoshi Ishiwata
    • Organizer
      Himeji Conference on Partial Differential Equations
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Poincare constant on manifold with ends2019

    • Author(s)
      S. Ishiwata
    • Organizer
      Analysis and PDEs on Manifolds and Fractals
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Poincare constant on manifolds with ends2018

    • Author(s)
      Satoshi Ishiwata
    • Organizer
      2018 Spring Probability Workshop, Institute of Mathematics, Academia Sinica
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Poincare Inequality on manifolds with ends2017

    • Author(s)
      Satoshi Ishiwata
    • Organizer
      Analysis and PDEs on Manifolds
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Poincare Inequality on manifolds with ends2017

    • Author(s)
      Satoshi Ishiwata
    • Organizer
      Global properties in potential theory of continuous and discrete spaces
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Poincare Inequality on manifolds with ends2017

    • Author(s)
      Satoshi Ishiwata
    • Organizer
      Cornell University Probability seminar
    • Related Report
      2017 Research-status Report
    • Invited

URL: 

Published: 2017-04-28   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi