Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary

Abstract

In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type problems for the convex capillary hypersurfaces and obtain the corresponding Alexandrov-Fenchel inequalities. In order to prove these results, we construct a new locally constrained curvature flow and prove that the flow converges globally to a spherical cap.

arXiv commentFinal version, to appear in Mathematische Annalen

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Cited by in corpus (10)

• A constrained mean curvature flow and Alexandrov-Fenchel inequalities
• 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
• A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
• Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces
• 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
• Monotonicity Formulas for Capillary Surfaces
• A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane