Geometry of metric measure spaces and optimal transport theory
Project/Area Number |
23740048
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Geometry
|
Research Institution | Kyoto University |
Principal Investigator |
OHTA Shin-ichi 京都大学, 理学(系)研究科(研究院), 准教授 (00372558)
|
Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | リーマン幾何 / 曲率 / 熱流 / フィンスラー幾何 / 勾配流 / リーマン幾何学 / 凸関数 / ハミルトン系 / アレクサンドロフ空間 / フィンスラー幾何学 / 最適輸送理論 |
Outline of Final Research Achievements |
We consider two generalizations of the curvature-dimension condition, which is a notion of a lower Ricci curvature bound for metric measure spaces. One generalization is to make the parameter regarded as an “upper bound of the dimension” being negative. Then the condition is getting weaker and covers a wider class of spaces. We also establish the Bochner formula for Finsler manifolds by using the weighted Ricci curvature. As applications, we obtain some gradient estimates for heat flow, and a generalization of Cheeger-Gromoll’s classical splitting theorem.
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Report
(5 results)
Research Products
(34 results)