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

TL;DR

This paper proves an Alexandrov-type theorem for singular capillary constant mean curvature hypersurfaces in the half-space, using a novel shifted distance function to handle the capillary problem.

Contribution

It introduces a new shifted distance function and establishes a classification theorem for singular capillary CMC hypersurfaces in the half-space.

Findings

Proved an Alexandrov-type theorem for singular capillary CMC hypersurfaces.

Developed a new shifted distance function suited for capillary problems.

Provided classification results under regularity assumptions.

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.