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

Jinyu Gao; Guanghan Li

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arXiv · 2507.04796

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

Jinyu Gao·Guanghan Li

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Abstract

In this paper, the results of Mei, Wang, Weng and Xia [Math. Z., 2025, MR4911815] on capillary convex bodies are extended to the anisotropic setting. We develop a theory for anisotropic capillary convex bodies in the half-space and establish a general Alexandrov-Fenchel inequality for mixed volumes of anisotropic capillary convex bodies. Thus, this weakens the conditions of the inequality in [Ding-Gao-Li,arXiv:2408.10740, Theorem 1.4] and extends it to a more general case.

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Jinyu Gao, Guanghan Li. 2025-07-07. Alexandrov-Fenchel inequalities for convex anisotropic capillary hypersurfaces in the half-space. https://arxiv.org/abs/2507.04796

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