Uniqueness of capillary Gauss solitons

Xinqun Mei; Guofang Wang; Liangjun Weng

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arXiv · 2608.22494

Uniqueness of capillary Gauss solitons

Xinqun Mei·Guofang Wang·Liangjun Weng

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Abstract

We prove the rigidity conjecture of [16, Conjecture 1.2] for smooth strictly convex capillary Gauss solitons in a Euclidean half-space with an acute contact angle: every such soliton is a spherical cap. Combined with our previous convergence result for the capillary Gauss curvature flow [16, Theorem 1.1], it follows that the flow starting from a strictly convex capillary hypersurface with an acute contact angle converges to a capillary spherical cap, after a suitable rescaling.

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Xinqun Mei, Guofang Wang, Liangjun Weng. 2026-08-23. Uniqueness of capillary Gauss solitons. https://arxiv.org/abs/2608.22494

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