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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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2011: ¥1,495,000 (Direct Cost: ¥1,150,000、Indirect Cost: ¥345,000)
Fiscal Year 2010: ¥1,625,000 (Direct Cost: ¥1,250,000、Indirect Cost: ¥375,000)
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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 / Gromov-Hausdorff収束 / 幾何学的測度論 / Ricci曲率 / 調和解析 / 関数解析 / リプシッツ関数 / ディリクレ形式 |
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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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Report
(3 results)
Research Products
(55 results)
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[Presentation] 調和関数と多様体の収束2011
Author(s)
本多正平
Organizer
研究集会 淡路島幾何学研究集会2011
Place of Presentation
淡路島 国民宿舎 慶野松原荘(招待講演)
Year and Date
2011-02-12
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