2012 Fiscal Year Final Research Report
Geometric properties on the threshold of the Sobolev type inequalities and generalization to metric spaces
| Project/Area Number |
21740034
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Yamagata University (2012)
University of Tsukuba (2009-2011) |
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Principal Investigator |
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| Research Collaborator |
KOTANI Motoko 東北大学, 大学院・理学研究科, 教授 (50230024)
KUMAGAI Takashi 京都大学, 理学部, 教授 (90234509)
OHTA Shin-ichi 京都大学, 理学部, 准教授 (00372558)
ALEXANDER Grigoryan ドイツ Bielefeld大学, 教授
THIERRY Coulhon オーストラリアAustralian National University, 教授
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| Project Period (FY) |
2009 – 2012
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| Keywords | 熱核の長時間挙動 / Poincare不等式 / Sobolev不等式 / 連結和 |
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| Research Abstract |
On non-compact Riemannian manifolds and infinite graphs, therelationship among global geometric structure, geometric inequalities and long time heatkernel behavior is well investigated by many researchers. In this research, we considerconnected sums and we obtain a precise relationship between a structure of bottlenecknessand isoperimetric inequality, Poincare inequality and long time heat kernel behavior.
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