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Harnack estimates for
the linear heat equation under the Ricci flow
Xiaorui Zhu |
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Vol. 252 (2011), No. 1, 245–256
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Abstract |
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We consider the linear heat equation on a manifold that evolves under the Ricci flow. The gradient estimates for positive solutions as well as Li–Yau type inequalities are given in this paper. Both the case where M is a complete manifold without boundary and the case where M is compact are considered. We have also obtained the Harnack inequalities for the heat equation on M by previous results. |
Keywords
linear heat equation, Harnack estimate
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Mathematical Subject Classification 2000
Primary: 53C44
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Milestones
Received: 16 August 2010
Revised: 30 November 2010
Accepted: 21 December 2010
Published: 8 October 2011
Proposed: Kefeng Liu
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Authors |
| Xiaorui Zhu | |
| Public Security Marine Police
Academy Ningbo 315801 China |
Center of Mathematical
Sciences ZheJiang University Hangzhou 310027 China |
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