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arXiv · 2403.19815

Anisotropic capillary hypersurfaces in a wedge

Hui Ma·Jiaxu Ma·Mingxuan Yang
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Abstract

We investigate anisotropic capillary hypersurfaces within a wedge in Euclidean space. In this study, we generalize the Minkowski norm \(F\), traditionally employed to define the anisotropic surface energy, to a gauge on the unit sphere \(S^n\). This generalization helps to illuminate a significant relationship between capillary hypersurfaces and hypersurfaces with free boundary. Our main results include new Minkowski formulae and a Heintze-Karcher type inequality. As an application, we prove an Alexandrov-type theorem, thereby extending the known results to the anisotropic setting.

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Hui Ma, Jiaxu Ma, Mingxuan Yang. 2024-03-28. Anisotropic capillary hypersurfaces in a wedge. https://arxiv.org/abs/2403.19815

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