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A Brunn-Minkowski inequality for the Hessian eigenvalue in three-dimensional convex domain |
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| Authors: | Pan Liu Lu Xu |
| Institution: | a Department of Mathematics, East China Normal University, Shanghai, 200241, China b Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province, China c Wuhan Institute of Physics and Mathematics, The Chinese Academy of Science, Wuhan, 430071, HuBei Province, China |
| Abstract: | We use the deformation methods to obtain the strictly log concavity of solution of a class Hessian equation in bounded convex domain in R3, as an application we get the Brunn-Minkowski inequality for the Hessian eigenvalue and characterize the equality case in bounded strictly convex domain in R3. |
| Keywords: | Constant rank theorem Hessian equation Eigenvalue Brunn-Minkowski inequality |
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