Heintze-Karcher inequality and capillary hypersurfaces in a wedge
Differential Geometry
2026-02-11 v2
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.
Keywords
Cite
@article{arxiv.2209.13839,
title = {Heintze-Karcher inequality and capillary hypersurfaces in a wedge},
author = {Xiaohan Jia and Guofang Wang and Chao Xia and Xuwen Zhang},
journal= {arXiv preprint arXiv:2209.13839},
year = {2026}
}
Comments
final version, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci