Acta mathematica scientia, Series B >
SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS
Received date: 2010-08-20
Online 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).
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
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 . DOI: 10.1016/S0252-9602(10)60187-7
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