Unknottedness of free boundary minimal surfaces and self-shrinkers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909932568182784 |
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| author | Chu, Sabine Franz, Giada |
| author_facet | Chu, Sabine Franz, Giada |
| contents | We study unknottedness for free boundary minimal surfaces in a three-dimensional Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary, and for self-shrinkers in the three-dimensional Euclidean space. For doing so, we introduce the concepts of boundary graph for free boundary minimal surfaces and of graph at infinity for self-shrinkers. We prove that these surfaces are unknotted in the sense that any two such surfaces with isomorphic boundary graph or graph at infinity are smoothly isotopic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unknottedness of free boundary minimal surfaces and self-shrinkers Chu, Sabine Franz, Giada Differential Geometry We study unknottedness for free boundary minimal surfaces in a three-dimensional Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary, and for self-shrinkers in the three-dimensional Euclidean space. For doing so, we introduce the concepts of boundary graph for free boundary minimal surfaces and of graph at infinity for self-shrinkers. We prove that these surfaces are unknotted in the sense that any two such surfaces with isomorphic boundary graph or graph at infinity are smoothly isotopic. |
| title | Unknottedness of free boundary minimal surfaces and self-shrinkers |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.16785 |