A flow method to isoperimetric inequality for mean convex star-shaped capillary hypersurfaces in a cone
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Point processes and geometric inequalities
Publication details
- Journal / source
- Differential Geometry and its Applications
- Volume
- 103
- Pages
- 102329–102329
- Publication date
- 14 January 2026
- Language
- EN