Alexandrov-type theorem for singular capillary CMC hypersurfaces in the half-space

Chao Xia; Xuwen Zhang

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arXiv · 2304.01735

Alexandrov-type theorem for singular capillary CMC hypersurfaces in the half-space

Chao Xia·Xuwen Zhang

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Abstract

In this paper, we consider the classification problem for critical points of relative isoperimetric-type problem in the half-space. Under certain regularity assumption, we prove an Alexandrov-type theorem for the singular capillary CMC hypersurfaces in the half-space. The key ingredient is a new shifted distance function that is suitable for the study of capillary problem in the half-space.

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Chao Xia, Xuwen Zhang. 2023-04-04. Alexandrov-type theorem for singular capillary CMC hypersurfaces in the half-space. https://arxiv.org/abs/2304.01735

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