Heintze-Karcher inequality and capillary hypersurfaces in a wedge

2022/09/28 by Xiaohan Jia, Jia, Xiaohan, Guofang Wang +5 · 4 citations
Engineering · Mathematics · #35J25 #3D Shape Modeling and Analysis #53C21 #53C24 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2209.13839

openalex publication_date 2022/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Prescribed L_p curvature problem for convex capillary hypersurface
• The capillary Christoffel-Minkowski problem
• Rigidity of critical points of hydrophobic capillary functionals
• The isoperimetric inequality for the capillary energy outside convex sets

Related

• Capillary hypersurfaces, Heintze-Karcher's inequality and Zermelo's navigation
• Anisotropic capillary hypersurfaces in a wedge
• Some rigidity results on compact hypersurfaces with capillary boundary in Hyperbolic space
• A Heintze-Karcher type inequality in hyperbolic space
• Stable capillary hypersurfaces in a wedge