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arXiv · 2206.04639

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

Guofang Wang·Liangjun Weng·Chao Xia
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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.

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Guofang Wang, Liangjun Weng, Chao Xia. 2022-06-09. Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary. https://doi.org/10.1007/s00208-023-02571-4

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