A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms

Abstract

In this paper, we introduce a new constrained mean curvature type flow for capillary boundary hypersurfaces in space forms. We show the flow exists for all time and converges globally to a spherical cap. Moreover, the flow preserves the volume of the bounded domain enclosed by the hypersurface and decreases the total energy. As a by-product, we give a flow proof of the capillary isoperimetric inequality for the starshaped capillary boundary hypersurfaces in space forms.

23pages

References in corpus (2)

• 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

Cited by in corpus (2)

• A mean curvature type flow with capillary boundary in a horoball in hyperbolic space
• A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane