2016 Fiscal Year Final Research Report
Heat kernel and geometric inequalities on spaces with bottle-neck structure
| Project/Area Number |
25800034
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Yamagata University |
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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)
KAWABI HITOSHI 岡山大学, 理学部, 教授 (80432904)
Grigor' yan Alexander Bielefeld大学, 教授
Saloff-Coste Laurent Cornell大学, 教授
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 熱核 |
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| Outline of Final Research Achievements |
Connected sums are known as manifolds without Li-Yau heat kernel estimate. In 2009, Grigor'yan and Saloff-Coste proved heat kernel estimates on manifolds with non-parabolic ends. In this research project, we obtain the heat kernel estimates on manifolds with parabolic ends. In particular, we proved that the on-diagonal value in the central part is determined by the maximal end, on the contrary to the case of manifolds with non-parabolic ends on which the on-diagonal value is determined by the minimal end. This shows that the heat kernel behavior on manifolds with parabolic ends are very different from that on manifolds with non-parabolic ends.
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| Free Research Field |
幾何解析
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