Geometric analysis and comparison geometry on weighted manifolds
| Project/Area Number |
20J11328
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 国内 |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Osaka University |
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Principal Investigator |
Mai Cong Hung 大阪大学, 理学研究科, 特別研究員(PD)
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| Project Period (FY) |
2020-04-24 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2021: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2020: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | Finsler manifolds / Berwald spaces / diffeomorphic splitting / rigidity / Bakry-Ledoux inequality / log sobolev / needle decomposition / isoperimetric inequality / weighted manifolds / noncompact manifolds / weighted Ricci curvature / L1-estimate |
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| Outline of Research at the Start |
My research focus on the geometric analysis aspect of weighted manifolds of lower Ricci curvature bound. The main topic of the project is isoperimetric inequalities and related estimates, including its rigidity and quantitative problems.
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| Outline of Annual Research Achievements |
During this research period, I study the studies on the rigidity of sharp spectral gaps in the setting of Finsler manifolds. I investigated the rigidity problem for the sharp spectral gap on Finsler manifolds and obtained the diffeomorphic splitting (or isometric splitting in the particular class of Berwald spaces). By analogous techniques to the Riemannian case, I also exhibit the rigidity results of logarithmic Sobolev and Bakry-Ledoux isoperimetric inequalities via needle decomposition for reversible Finsler manifolds. This splitting phenomenon is comparable to the Cheeger-Gromoll type splitting theorem by Ohta.
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| Research Progress Status |
令和3年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和3年度が最終年度であるため、記入しない。
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Report
(2 results)
Research Products
(4 results)
