Study of metric measure spaces with curvature-dimension conditions and its applications to Riemannian geometry
| Project/Area Number |
18K13412
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Kumamoto University |
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Principal Investigator |
Kitabeppu Yu 熊本大学, 大学院先端科学研究部(理), 准教授 (50728350)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 熱流 / RCD 空間 / 曲率次元条件 / 非線形ラプラシアン / 最大直径定理 / Gromov-Hausdorff 収束 / Ricci 曲率 / リーマン的曲率次元条件 / Wasserstein 距離 / Symplectic toric 多様体 / リーマン幾何学 |
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| Outline of Final Research Achievements |
It is known that we can use much techniques of calculus on RCD spaces, which can be applied to wide class including collapsed manifolds.
Roughly, we have the following two results: One is the Zhong-Yang type rigidity theorem for RCD spaces, and another is giving a definition of Ricci curvature on hypergraphs associated with the heat flow.
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| Academic Significance and Societal Importance of the Research Achievements |
ハイパーグラフはネットワークのモデルなどとしてよく使われており、特に近年ハイパーグラフ上の熱の伝わりかたに関する研究もよくされている。ハイパーグラフ上に熱流、正確にいえば非線形ラプラシアンから定まるレゾルベント、を用いた曲率の定義を与えたことで、今後ハイパーグラフ上の現実的な問題に関しても応用があると期待される。
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Report
(6 results)
Research Products
(16 results)
