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arXiv · 2401.12137

Generalized Minkowski formulas and rigidity results for anisotropic capillary hypersurfaces

Jinyu Gao·Guanghan Li
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Abstract

In this paper, we obtain a new Hsiung-Minkowski integral formula for anisotropic capillary hypersurfaces in the half-space, which includes the weighted Hsiung-Minkowski formula and classical anisotropic Minkowski identity for closed hypersurfaces as special cases. As applications, we prove some anisotropic Alexandrov-type theorems and rigidity results for anisotropic capillary hypersurfaces. Specially, the uniqueness of the solution to the anisotropic Orlicz-Christoffel-Minkowski problem is obtained, and thus a new proof is provided for the uniqueness of the solution to $L_p$-Minkowski problem with $p\geq 1$ in the Euclidean capillary convex bodies geometry.

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Jinyu Gao, Guanghan Li. 2024-01-22. Generalized Minkowski formulas and rigidity results for anisotropic capillary hypersurfaces. https://arxiv.org/abs/2401.12137

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