2015 Fiscal Year Final Research Report
Towerd analysis on metric-measure spaces-- Cheeger theory and fractals
Project/Area Number |
26610023
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Kyoto University |
Principal Investigator |
Kigami Jun 京都大学, 情報学研究科, 教授 (90202035)
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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)
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Project Period (FY) |
2014-04-01 – 2016-03-31
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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.
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Free Research Field |
基礎解析一般(含関数空間論・応用解析の基礎)
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