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 Alexandrov-type theorems in convex cones.