Alexandrov's theory for anisotropic capillary hypersurfaces in half space

Title: Alexandrov's theory for anisotropic capillary hypersurfaces in half space

Speaker: Professor Xia Chao (Xiamen University)

Time: Tuesday, April 18, 2023, 10:00 am

Location: 105, Building 2, Hainayuan

Abstract: The minimizers for surface free energy functional, which is the sum of anisotropic surface tension (or parametric elliptic functional) and the wetting energy functional, in half-space are known to be truncated Wulff shapes. The anisotropic capillary hypersurfaces arise as the critical points of the free energy functional under volume constraint. In this talk, we prove an Alexandrov-type theorem saying that any embedded anisotropic capillary hypersurfaces in half-space are truncated Wulff shapes. The main ingredients are a Heintze-Karcher-type inequality and a Minkowski-type formula. The talk is based on a joint work with Xiaohan Jia, Guofang Wang and Xuwen Zhang.