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Towerd analysis on metric-measure spaces-- Cheeger theory and fractals

Research Project

Project/Area Number 26610023
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionKyoto University

Principal Investigator

Kigami Jun  京都大学, 情報学研究科, 教授 (90202035)

Co-Investigator(Renkei-kenkyūsha) Kumagai Takashi  京都大学, 数理解析研究所, 教授 (90234509)
Hino Masanori  大阪大学, 大学院基礎工学研究科, 教授 (40303888)
Kajino Naotaka  神戸大学, 大学院理学研究科, 准教授 (90700352)
Project Period (FY) 2014-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords解析学 / フラクタル / 測度論リーマン構造 / 測度・距離空間 / Dirichlet form / partition / quasisymmetry / volume doubling property / 測度論的リーマン構造 / Dirichlet From / 自己相似集合 / tree / 距離空間 / quaisymmetry
Outline of Final Research Achievements

To study analysis on metric-measure spaces, we have investigated important properties of metrics and measures on topological space such as bi-Lipshitz equivalence, volume doubling property, quasisymmetry and Ahlfors regularity form the view point of partitions and associated gauge functions. In particular, we have shown that bi-Lipshitz property between a measure and a metric as gauge functions is equivalent to the Ahlfors regularity between a measure and a metric.

Report

(3 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • Research Products

    (4 results)

All 2015 2014 Other

All Int'l Joint Research (1 results) Presentation (3 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results)

  • [Int'l Joint Research] University of Jyvaskyla(Finland)

    • Related Report
      2015 Annual Research Report
  • [Presentation] Partition of metrizable spaces by trees, volume doubling measures and quasisymmetry2015

    • Author(s)
      木上 淳
    • Organizer
      America Mathematical Society sectional meeting #1114,
    • Place of Presentation
      California State University, (Fullerton, CA, USA)
    • Year and Date
      2015-10-24
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Self-similar sets as quotients of shifts2014

    • Author(s)
      Jun Kigami
    • Organizer
      New Directions in Fractal Geometry
    • Place of Presentation
      Australian National University, Canberra, Australia
    • Year and Date
      2014-11-24 – 2014-11-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Self-similar sets as quotients of shift spaces2014

    • Author(s)
      Jun Kigami
    • Organizer
      5th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals
    • Place of Presentation
      Cornell University, Ithaca, NY, USA
    • Year and Date
      2014-06-11 – 2014-06-15
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2017-05-10  

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