Uniqueness of capillary disks in three-dimensional domains
Differential Geometry
2026-03-30 v1
Abstract
We prove uniqueness results for capillary disks in three-dimensional domains that are modeled by an elliptic PDE, under the assumption that the domain admits a family of surfaces with suitable properties. Our main theorem generalizes Nitsche's result for capillary constant mean curvature disks in the Euclidean ball and is inspired by the extension of Hopf's uniqueness theorem for constant mean curvature spheres in Euclidean space due to G\'alvez and Mira.
Keywords
Cite
@article{arxiv.2603.25929,
title = {Uniqueness of capillary disks in three-dimensional domains},
author = {Henrique Nogueira Bastos},
journal= {arXiv preprint arXiv:2603.25929},
year = {2026}
}