Heintze-Karcher Inequality for Anisotropic Free Boundary Hypersurfaces in Convex Domains

Authors

  • Xiaohan Jia
  • Guofang Wang
  • Chao Xia
  • Xuwen Zhang

DOI:

https://doi.org/10.4208/jms.v57n3.24.01

Keywords:

Heintze-Karcher’s inequality, constant mean curvature, free boundary surface, capillary surface, convex cone.

Abstract

In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic free boundary Wulff shapes in a convex cone. As applications, we prove Alexandrov-type theorems in convex cones.

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Published

2024-10-31

Issue

Vol. 57 No. 3 (2024)

Section

Articles