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arXiv · 2209.13839

Heintze-Karcher inequality and capillary hypersurfaces in a wedge

Xiaohan Jia·Guofang Wang·Chao Xia·Xuwen Zhang
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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.

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Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhang. 2023-12-05. Heintze-Karcher inequality and capillary hypersurfaces in a wedge. https://doi.org/10.2422/2036-2145.202212_001

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