Work

A flow method to isoperimetric inequality for mean convex star-shaped capillary hypersurfaces in a cone

Year: 2026

Type: article

Abstract: In this paper, the Minkowski formula and the Heintze-Karcher inequality are obtained for hypersurfaces with capillary boundary in a cone. Then we study a type of inverse mean curvature flow in a cone, as well as its long-time existence and convergence. As a result we derive the capillary isoperimetric inequality for mean convex star-shaped hypersurfaces with capillary boundary in a cone.

Source: Differential Geometry and its Applications

DOI: 10.1016/j.difgeo.2025.102329

Authors: Guanghan Li, Yifan Yang

Institution: Wuhan University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,740

Funder: National Natural Science Foundation of China