Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow

Abstract

In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as $t\to +\infty$

24 pages, 1 figure

References in corpus (9)

• Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
• A fully-nonlinear flow and quermassintegral inequalities in the sphere
• 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
• Volume preserving flow by powers of $k$-th mean curvature
• A constrained mean curvature flow and Alexandrov-Fenchel inequalities
• Quantitative isoperimetric inequalities for classical capillarity problems
• A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
• A Minkowski-type inequality for capillary hypersurfaces in a half-space