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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/2605.08487 |
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| _version_ | 1866917474960670720 |
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| author | Cardona, Carlos Andrés Toro |
| author_facet | Cardona, Carlos Andrés Toro |
| contents | We investigate complete non-orientable minimal surfaces of finite total curvature in $\mathbb{R}^3$ such that their ends are foliated by closed lines of curvature. This condition on the ends is necessary if they have a piece inside some Euclidean ball that is free boundary. It turns out this is a rigid situation, and we are able to show, among further obstructions, that there are no such surfaces with one end. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal surfaces with closed curvature lines Cardona, Carlos Andrés Toro Differential Geometry We investigate complete non-orientable minimal surfaces of finite total curvature in $\mathbb{R}^3$ such that their ends are foliated by closed lines of curvature. This condition on the ends is necessary if they have a piece inside some Euclidean ball that is free boundary. It turns out this is a rigid situation, and we are able to show, among further obstructions, that there are no such surfaces with one end. |
| title | Minimal surfaces with closed curvature lines |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.08487 |