Alexandrov’s Theorem for Anisotropic Capillary Hypersurfaces in the Half-Space

Abstract

AbstractIn this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente’s result (Pac J Math 88:387–397, 1980. https://doi.org/10.2140/pjm.1980.88.387) to the anisotropic case and He–Li–Ma–Ge’s result (Indiana Univ Math J 58(2):853–868, 2009. https://doi.org/10.1512/iumj.2009.58.3515) to the capillary boundary case. The main ingredients in the proof are a new Heintze-Karcher inequality and a new Minkowski formula, which have their own interest.