| Yamabe流下黎曼流形上热方程的梯度估计 |
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| 引用本文： | 杨飞,沈婧芳.Yamabe流下黎曼流形上热方程的梯度估计[J].数学年刊A辑(中文版),2013,34(1):101-110. |
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| 作者姓名： | 杨飞 沈婧芳 |
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| 作者单位： | 中国地质大学(武汉)数学与物理学院;华中农业大学理学院 |
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| 基金项目： | 中国地质大学(武汉)中央高校基本科研业务费专项资金(No.CUGK120224)的资助 |
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| 摘 要： | 研究了在Yamabe流下演化的一个完备非紧黎曼流形,对流形上热方程的正解给出了两种局部的梯度估计.作为应用,可以得到这个热方程的Harnack不等式.
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| 关 键 词： | Yamabe流 热方程 梯度估计 |
Gradient Estimate for the Heat Equation on Riemannian Manifolds under the Yamabe Flow |
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| YANG Fei and SHEN Jingfang.Gradient Estimate for the Heat Equation on Riemannian Manifolds under the Yamabe Flow[J].Chinese Annals of Mathematics,2013,34(1):101-110. |
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| Authors: | YANG Fei and SHEN Jingfang |
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| Institution: | 1 School of Mathematics and Physics,China University of Geosciences(Wuhan), Wuhan 430000,China. 2 Corresponding author.College of Science,Huazhong Agricultural University, Wuhan 430000,China. |
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| Abstract: | The authors study a complete noncompact Riemannian manifold evolving under the Yamabe flow and derive two versions of localized gradient estimates for positive solutions to the heat equation on the evolving manifold. As an application, the Harnack inequality for the heat equation can be established immediately. |
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| Keywords: | Yamabe flow Heat equation Gradient estimate |
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