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

2015 Fiscal Year Final Research Report

• Project/Area Number: 26610023
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyoto 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
• 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

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.

Free Research Field

基礎解析一般（含関数空間論・応用解析の基礎）