The study of collapsing Riemannian manifolds related to Ricci curvature
Project/Area Number |
24740046
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
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Research Institution | Tohoku University (2015) Kyushu University (2012-2014) |
Principal Investigator |
Honda Shouhei 東北大学, 理学(系)研究科(研究院), 准教授 (60574738)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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)
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Keywords | Ricci曲率 / ラプラシアン / Ricci curvature / Laplacian / Gromov-Hausdorff収束 / リッチ曲率 / p-Laplacian / Cheeger等周定数 / Gromov-Hausdorr収束 |
Outline of Final Research Achievements |
I studied the Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a lower Ricci curvature bound via functional analytic methods. In particular we introduce the notion of Lp-convergence with respect to the Gromov-Hausdorff convergence, prove regularities of limit spaces via the convergence theory, and give applications of them to Riemannian geometry.
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Report
(5 results)
Research Products
(59 results)