Work

Willmore‐type inequality in unbounded convex sets

Year: 2025

Type: article

Abstract: In this paper, we prove the following Willmore‐type inequality: on an unbounded closed convex set ), for any embedded hypersurface with boundary satisfying a certain contact angle condition, there holds Moreover, equality holds if and only if a part of a sphere and is a part of the solid cone determined by . Here, is the bounded domain enclosed by and , is the normalized mean curvature of , and is the asymptotic volume ratio of . We also prove an anisotropic version of this Willmore‐type inequality. As a special case, we obtain a Willmore‐type inequality for anisotropic capillary hypersurfaces in a half‐space.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70105

Authors: Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhang

Institutions: Southeast University, University of Freiburg, Xiamen University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: National Natural Science Foundation of China, Natural Science Foundation of Jiangsu Province