Heat kernel and geometric inequalities on spaces with bottle-neck structure
| Project/Area Number |
25800034
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Yamagata University |
|---|
Principal Investigator |
|
|---|
| 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
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | 熱核 / 推移確率 / 連結和 / parabolicity / 中心極限定理 / 非対称ランダム・ウォーク / ランダム・ウォーク / 結晶格子 |
|---|
| 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.
|
Report
(5 results)
Research Products
(24 results)
