Heintze-Karcher Inequality for Anisotropic Free Boundary Hypersurfaces in Convex Domains (Journal of Mathematical Study, 2024)
In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality isachieved for anisotropic free boundary Wulff shapes in a convex cone. As applications, we prove Alexandrov-type theorems in convex cones.
Keywords: Heintze-Karcher’s inequality; constant mean curvature; free boundary surface; capillary surface; convex cone.