2010 Fiscal Year Final Research Report
Geometry of the space of probability measures and its applications
| Project/Area Number |
20740036
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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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 |
OHTA Shin-Ichi Kyoto University, 大学院・理学研究科, 准教授 (00372558)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 曲率 / リーマン幾何学 / フィンスラー幾何学 / 最適輸送理論 / 熱流 |
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| Research Abstract |
We studied the geometry of Wasserstein spaces, which are the metric spaces consisting of probability measures on metric spaces. One of our achievements is the investigation of the geometric structure of the Wasserstein space over a possibly highly singular space (an Alexandrov space), and the establishment of the theory of gradient flows in such a space. We also generalized the known equivalence between the convexity of a certain entropy on the Wasserstein space and a curvature bound of the underlying space to a wider class of spaces (Finsler manifolds).
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