A mean curvature type flow with capillary boundary in a unit ball

Abstract

In this paper, we study a mean curvature type flow with capillary boundary in the unit ball. Our flow preserves the volume of the bounded domain enclosed by the hypersurface, and monotonically decreases an energy functional $E$. We show that it has the longtime existence and subconverges to spherical caps. As an application, we solve an isoperimetric problem for hypersurfaces with capillary boundary.

28 pages with some revisions: typos are corrected, rewrite Section 2.2, notations are unified and presentations are simplified. To appear in Calc. Var. Partial Differential Equations

References in corpus (2)

• Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
• Guan-Li type mean curvature flow for free boundary hypersurfaces in a ball

Cited by in corpus (7)

• 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
• On the mean curvature type flow for convex capillary hypersurfaces in the ball
• A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
• 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