Comparison geometry of Ricci flow and Ricci solitons
| Project/Area Number |
22840028
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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 |
YOKOTA Takumi 京都大学, 数理解析研究所, 助教 (70583855)
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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 | リッチ流 / アレクサンドロフ空間 / ワッサーシュタイン空間 |
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| Research Abstract |
In this research, we mainly studied geometries of the Ricci fow and Alexandrov spaces of curvature bounded below, and we refined our gap theorem for gradient shrinking Ricci solitons, which are self-similar solutions to the Ricci flow equation. We also proved comparison and rigidity theorems stating that the filling radius of any finite-dimensional Alexandrov space with a positive lower curvature bound is at most that of the round sphere, and the equality holds if and only if it is isometric to the round sphere.
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Report
(3 results)
Research Products
(15 results)
