2017 Fiscal Year Final Research Report
Generalization of the Ricci flow
Project/Area Number |
25400074
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
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Research Institution | Tohoku University (2016-2017) Osaka University (2013-2015) |
Principal Investigator |
|
Co-Investigator(Kenkyū-buntansha) |
都築 正男 上智大学, 理工学部, 教授 (80296946)
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Project Period (FY) |
2013-04-01 – 2018-03-31
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Keywords | リッチフロー / 熱方程式 |
Outline of Final Research Achievements |
We proved the differential Harnack inequality for the geometric flow in abstract setting. As a corollary, we obtained a new differential Harnack inequality for positive solutions to the conjugate heat equations associated with the Ricci flow coupled with harmonic map heat flow. We also proved a new differential Harnack inequality for the Ricci Yang-Mills flow on surface. Moreover, we introduced a reduced volume type quantity for the Ricci Yang-Mills flow on surface and proved its monotonicity under the flow. Under a mild condition on the curvature,we also proved a Perelman type no local collapsing theorem for the Ricci Yang-Mills flow in general dimension.
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Free Research Field |
幾何学
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