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 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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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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| Project Status |
Completed (Fiscal Year 2015)
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| 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)
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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 / 測度論的リーマン構造 / Dirichlet From / 自己相似集合 / tree / 距離空間 / quaisymmetry |
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| 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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Report
(3 results)
Research Products
(4 results)
