# American Institute of Mathematical Sciences

November  2014, 13(6): 2305-2316. doi: 10.3934/cpaa.2014.13.2305

## Mirror symmetry for a Hessian over-determined problem and its generalization

 1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received  September 2013 Revised  February 2014 Published  July 2014

In the paper, we apply the moving plane method to prove that if the right hand sides of equation and Neumann boundary condition are both independent of one variable, the domain and the solution to the Hessian over-determined problem are mirror symmetric. Our result generalizes the previous results on radial symmetry. In the end, we get the mirror symmetry of over-determined problems for more general equations, which include Weingarten curvature equation.
Citation: Bo Wang, Jiguang Bao. Mirror symmetry for a Hessian over-determined problem and its generalization. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2305-2316. doi: 10.3934/cpaa.2014.13.2305
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