Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space

Abstract

In 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 \cite{Wente80} to the anisotropic case and He-Li-Ma-Ge's result \cite{HLMG09} 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 inetrest.

16 pages

References in corpus (2)

• Heintze-Karcher inequality and capillary hypersurfaces in a wedge
• Minimizers of Anisotropic Surface Tensions Under Gravity: Higher Dimensions via Symmetrization

Cited by in corpus (7)

• Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains
• Capillary Schwarz symmetrization in the half-space
• Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces
• A fully nonlinear locally constrained curvature flow for capillary hypersurface
• Stability of the Wulff shape with respect to anisotropic curvature functionals
• Monotonicity Formulas for Capillary Surfaces
• Willmore-type inequality in unbounded convex sets