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arXiv · 2111.05773

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

Liangjun Weng·Chao Xia
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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 $\mathbb{B}^{n+1}$.

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Liangjun Weng, Chao Xia. 2021-11-10. Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball. https://doi.org/10.1090/tran%2F8756

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