A Minkowski-type inequality for capillary hypersurfaces in a half-space

Abstract

In this article, we investigate a flow of inverse mean curvature type for capillary hypersurfaces in the half-space. We establish the global existence of solutions for this flow and demonstrate that it converges smoothly to a spherical cap as time tends to infinity. As a result, we derive a new Minkowski-type inequality for star-shaped and mean convex capillary hypersurfaces for the whole range of contact angle $\theta \in (0,\pi )$.

To appear in JFA. Minor revision based on referees' report

References in corpus (4)

• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• A constrained mean curvature flow and Alexandrov-Fenchel inequalities
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space

Cited by in corpus (3)

• A fully nonlinear locally constrained curvature flow for capillary hypersurface
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
• Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow