2012 Fiscal Year Final Research Report
Geometric application of concentration of measure phenomenon
| Project/Area Number |
23840020
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
FUNANO Kei 京都大学, 大学院・理学研究科, 助教 (40614144)
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| Co-Investigator(Renkei-kenkyūsha) |
SHIOYA Takashi 東北大学, 大学院・理学研究科, 教授 (90235507)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 測度の集中 / ラプラシアン |
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| Research Abstract |
We studied properties of eigenavalues of Laplacian on closed Riemannian manifolds of nonnegative Ricci curvature. One of our achievements is the k-th non-trivial eigenvalue of Laplacian on such manifolds is bounded by the first eigenvalue times universal constant depending only on k. In our proof, we obtained a stability result of curvature-dimension condition under concentration topology. This result extends the known-result that cuvature-dimension condition is stable under the measured Gromov-Hausdorff topology.
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