On the uniqueness of stable anisotropic capillary hypersurfaces that contact the edge of a wedge

Abstract

Anisotropic energies serve to model the boundaries of some types of crystals and liquid crystals. We study the stability of capillary hypersurfaces with anisotropic energy in a wedge, which contact with the edge of the wedge. We prove that stable capillary hypersurfaces in a wedge are, up to rescaling, only parts of the Wulff shape under some boundary conditions. Here the Wulff shape is the model of a single crystal introduced by G. Wulff.