ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

doi:10.1016/S0252-9602(11)60358-5

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1741-1748.doi: 10.1016/S0252-9602(11)60358-5

ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

谭忠|吴国春^*

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

收稿日期:2010-06-28 出版日期:2011-09-20 发布日期:2011-09-20
通讯作者: 吴国春,guochunwu@126.com E-mail:ztan85@163.com; guochunwu@126.com
基金资助:
Supported by NSFC (10976026).

ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

TAN Zhong, WU Guo-Chun^*

School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2010-06-28 Online:2011-09-20 Published:2011-09-20
Contact: WU Guo-Chun,guochunwu@126.com E-mail:ztan85@163.com; guochunwu@126.com
Supported by:
Supported by NSFC (10976026).

摘要/Abstract

摘要：

In this paper, we consider the heat flow for the H-system with constant mean curvature in higher dimensions. We give sufficient conditions on the initial data such that the heat flow develops finite time singularity. We also provide a new set of initial data to
guarantee the existence of global regular solution to the heat flow, that converges to zero in W^{1, n} with the decay rate t^2/2−nas time goes to infinity.

关键词: heat equation, mean curvature, higher dimensions

Abstract:

Key words: heat equation, mean curvature, higher dimensions

中图分类号:

35Q99

谭忠, 吴国春. ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS[J]. 数学物理学报(英文版), 2011, 31(5): 1741-1748.

TAN Zhong, WU Guo-Chun. ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS[J]. Acta mathematica scientia,Series B, 2011, 31(5): 1741-1748.

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ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

ON THE HEAT FLOW EQUATION OF SURFACES OF CONSTANT MEAN CURVATURE IN HIGHER DIMENSIONS

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