Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports

Caiyan Li; Chao Xia

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arXiv · 2609.10318

Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports

Caiyan Li·Chao Xia

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Abstract

In this paper, we prove that, under suitable conditions on the generating profile, every connected, compact embedded minimal capillary hypersurface supported on a one-ended rotational hypersurface in the Euclidean space is a horizontal slice. We also construct a smooth one-ended rotational support carrying a non-horizontal planar capillary $n$-ball, showing that the main slope condition cannot in general be omitted. For obtuse contact angles, we further obtain a catenoid-band classification under a reverse profile inequality.

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BibTeX RIS

Caiyan Li, Chao Xia. 2026-09-09. Alexandrov-Type Rigidity for Minimal Capillary Hypersurfaces on Rotational Supports. https://arxiv.org/abs/2609.10318

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