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

• 论文 • 上一篇    下一篇

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

谭忠|吴国春*   

  1. 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*   

  1. 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:

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 W1, n with the decay rate t2/2−n as time goes to infinity.

关键词: heat equation, mean curvature, higher dimensions

Abstract:

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 W1, n with the decay rate t2/2−n as time goes to infinity.

Key words: heat equation, mean curvature, higher dimensions

中图分类号: 

  • 35Q99