数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 2006-2016.doi: 10.1016/S0252-9602(10)60187-7

• 论文 • 上一篇    下一篇

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

简怀玉, 鞠红杰, 刘艳楠, 孙伟   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China Department of Applied Mathematics, Beijing Technology and Business University, Beijing 100048, China Department of Mathematics, Ohio State University, Columbus 43210, USA
  • 收稿日期:2010-08-20 出版日期:2010-11-20 发布日期:2010-11-20
  • 基金资助:

    Supported by Natural Science Foundation of China (10631020,  10871061) and the Grant for Ph.D Program of Ministry of Education of China. Liu is supported by Innovation Propject for the Development of Science and Technology (IHLB) (201098).

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

 JIAN Huai-Yu, JU Hong-Jie, LIU Yan-Nan, SUN Wei   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China Department of Applied Mathematics, Beijing Technology and Business University, Beijing 100048, China Department of Mathematics, Ohio State University, Columbus 43210, USA
  • Received:2010-08-20 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    Supported by Natural Science Foundation of China (10631020,  10871061) and the Grant for Ph.D Program of Ministry of Education of China. Liu is supported by Innovation Propject for the Development of Science and Technology (IHLB) (201098).

摘要:

First, we review the authors' recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric  solutions.  Then we study the sufficient condition  for which  the translating solution is rotationally symmetric. We will use  a moving plane method  to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.

关键词: mean curvature flow, symmetry, fully nonlinear, elliptic equation

Abstract:

First, we review the authors' recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric  solutions.  Then we study the sufficient condition  for which  the translating solution is rotationally symmetric. We will use  a moving plane method  to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.

Key words: mean curvature flow, symmetry, fully nonlinear, elliptic equation

中图分类号: 

  • 35J65