A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space

Abstract

In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with $\theta$-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle $\theta \in (0,\pi /2]$. We prove that the solution of the flow remains to be strictly convex for $t>0$, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle $\theta \in (0,\pi /2]$. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.

v2, 28 pages, 2 figures

References in corpus (4)

• Locally constrained curvature flows and geometric 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

Cited by in corpus (5)

• A Minkowski-type inequality for capillary hypersurfaces in a half-space
• 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
• A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane