Heintze-Karcher inequality and capillary hypersurfaces in a wedge

Abstract

In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial ingredients in the proof is modified parallel hypersurfaces which are very natural to be used to study capillary hypersurfaces. A more technical part is a subtle analysis along the edge of a wedge. As an application, we classify completely embedded capillary constant mean curvature hypersurfaces that hit the edge in a wedge, which is a subtler case.

final version, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci

Cited by in corpus (8)

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• A Heintze-Karcher type inequality for hypersurfaces with capillary boundary
• Capillary Schwarz symmetrization in the half-space
• A fully nonlinear locally constrained curvature flow for capillary hypersurface
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
• Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces
• Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
• Willmore-type inequality in unbounded convex sets