SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS  

作　　者：简怀玉 鞠红杰 刘艳楠 孙伟 

机构地区：[1]Department of Mathematical Sciences, Tsinghua University [2]Department of Applied Mathematics, Beijing Technology and Business University [3]Department of Mathematics, Ohio State University

出　　处：《Acta Mathematica Scientia》2010年第6期2006-2016,共11页数学物理学报（B辑英文版）

基　　金：Supported by Natural Science Foundation of China (10631020, 10871061);the Grant for Ph.D Program of Ministry of Education of China;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.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 

分 类 号：O186.11[理学—数学]