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

Weng, Liangjun; Xia, Chao

doi:10.1090/tran/8756

Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
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Trans. Amer. Math. Soc. 375 (2022), 8851-8883 Request permission

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 of Scheuer [J. Differential Geom. 120 (2022), pp. 345–373] for convex hypersurfaces with free boundary in ${\mathbb {B}}^{n+1}$.

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