SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

doi:10.1016/S0252-9602(10)60187-7

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

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

简怀玉, 鞠红杰, 刘艳楠, 孙伟

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

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/Abstract

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:

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

中图分类号:

35J65

简怀玉, 鞠红杰, 刘艳楠, 孙伟. SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS[J]. 数学物理学报(英文版), 2010, 30(6): 2006-2016.

JIAN Huai-Yu, JU Hong-Jie, LIU Yan-Nan, SUN Wei. SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS[J]. Acta mathematica scientia,Series B, 2010, 30(6): 2006-2016.

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SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

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