PreprintCC BY-NC-ND 4.0arXiv
Uniqueness of capillary Gauss solitons
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.
Related
- The capillary 𝐿_{𝑝}-Minkowski problem
- The Implicit Combinatorial Bijection in Gauss's Article 148 of the Disquisitiones Arithmeticae
- Stable Capillary Minimal Hypersurfaces in R4+
- Hopf-Nitsche-type theorem for anisotropic capillary disks in a half 3-space
- Congruence theorems for capillary hypersurfaces and a substatic Heintze--Karcher inequality
BibTeX
@misc{mei2026uniqueness,
title = {{Uniqueness of capillary Gauss solitons}},
author = {Xinqun Mei and Guofang Wang and Liangjun Weng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.22494},
eprint = {2608.22494},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22494},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Uniqueness of capillary Gauss solitons
AU - Xinqun Mei
AU - Guofang Wang
AU - Liangjun Weng
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.22494
UR - https://arxiv.org/abs/2608.22494
AB - 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.
ER -