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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.25929 |
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| _version_ | 1866914425951223808 |
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| author | Bastos, Henrique Nogueira |
| author_facet | Bastos, Henrique Nogueira |
| contents | 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 Gálvez and Mira. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness of capillary disks in three-dimensional domains Bastos, Henrique Nogueira Differential Geometry 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 Gálvez and Mira. |
| title | Uniqueness of capillary disks in three-dimensional domains |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.25929 |