偏微分方程系列报告之01【夏　超】

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 introduce two rigidity results on anisotropic capillary hypersurfaces. One is an Alexandrov-type theorem saying that any embedded anisotropic capillary hypersurfaces in half-space are truncated Wulff shapes. The other is that any stable anisotropic capillary hypersurfaces in half-space are truncated Wulff shapes. 

The talk is based on a joint work with Jia-Wang-Zhang and another joint work with Guo.