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.

15 pages, 1 figure

References in corpus (2)

• Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space
• Capillary Schwarz symmetrization in the half-space

Cited by in corpus (2)

• Monotonicity Formulas for Capillary Surfaces
• Willmore-type inequality in unbounded convex sets