Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains
Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhang
TL;DR
This paper establishes an optimal inequality for anisotropic free boundary hypersurfaces in convex domains, with equality characterized by anisotropic Wulff shapes, and applies it to prove Alexandrov-type theorems.
Contribution
It introduces a new Heintze-Karcher inequality for anisotropic free boundary hypersurfaces in convex domains, extending classical geometric inequalities.
Findings
Proved an optimal Heintze-Karcher inequality for anisotropic free boundary hypersurfaces.
Characterized equality cases as anisotropic Wulff shapes in convex cones.
Derived Alexandrov-type theorems as applications.
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 various Alexandrov-type theorems.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Analytic and geometric function theory · Geometric Analysis and Curvature Flows