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.

Final version, to appear in Mathematische Annalen

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