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Gradient estimates
for positive solutions of the heat equation under geometric
flow
Jun Sun |
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Vol. 253 (2011), No. 2, 489–510
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Abstract |
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We establish first- and second-order gradient estimates for positive solutions of the heat equations under general geometric flows. Our results generalize the recent work of S. Liu, who established similar results for the Ricci flow. Both results can also be considered as the generalization of P. Li, S. T. Yau, and J. Li’s gradient estimates under geometric flow setting. We also give an application to the mean curvature flow. |
Keywords
gradient estimate, geometric flow, heat equation, Harnack
inequality
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Mathematical Subject Classification 2000
Primary: 53C44, 58J35
Secondary: 53C21, 35K55
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Milestones
Received: 4 September 2009
Revised: 14 January 2010
Accepted: 12 April 2010
Published: 21 January 2012
Proposed: Jie Qing
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Authors |
| Jun Sun | |
| Institute of Mathematics Academy of Mathematics and Systems Science, Chinese Academy of Sciences 55 Zhongguancun East Road Beijing 100190 China |
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