2011 Fiscal Year Final Research Report
The geometry related to Ricci curvature
| Project/Area Number |
22840027
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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 | Kyushu University (2011)
Kyoto University (2010) |
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Principal Investigator |
HONDA Shouhei 九州大学, 数理学研究院, 助教 (60574738)
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| Project Period (FY) |
2010 – 2011
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| Keywords | リッチ曲率 / ラプラシアン / グロモフ・ハウスドルフ収束 |
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| Research Abstract |
Let$ Y$ be a GromovHausdorff limit space of a sequence of complete Riemannian manifolds with a lower Ricci curvature bound. Then we have the following : 1. If the one-dimensional regular set of$ Y$ is nonempty, then$ Y$ is isometric to a onedimensional complete Riemannian manifold(with boundary). 2. Let$\gamma_1,\gamma_2$ be a minimal geodesics on$ Y$ beginning at a fixed point$ p\in Y$. Then the angle between$\gamma_i$ at$ p$ is well defined as long as they can be extended minimally through$ p$. 3.$ Y$ has a weakly second differentiable structure and there exists a unique LeviCivita connection on$ Y$. Every eigenfunction with respect to the Dirichlet problem on$ Y$ is second differentiable.
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