Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains

Abstract

In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic free boundary Wulff shapes in a convex cone. As applications, we prove various Alexandrov-type theorems.Comment: 15 pages, 1 figur