Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball

Abstract

In this paper, we first introduce the quermassintegrals for convex hypersurfaces with capillary boundary in the unit Euclidean ball ${\mathbb{B}}^{n+1}$ and derive its first variational formula. Then by using a locally constrained nonlinear curvature flow, which preserves the $n$-th quermassintegral and non-decreases the $k$-th quermassintegral, we obtain the Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in ${\mathbb{B}}^{n+1}$. This generalizes the result in \cite{SWX} for convex hypersurfaces with free boundary in ${\mathbb{B}}^{n+1}$.

To appear in Trans. Amer. Math. Soc

References in corpus (2)

• A fully-nonlinear flow and quermassintegral inequalities in the sphere
• Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities

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• A constrained mean curvature type flow for capillary boundary hypersurfaces in space forms
• 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
• A mean curvature type flow with capillary boundary in a horoball in hyperbolic space
• A Minkowski type inequality with free boundary in space forms