Dihedralization of Minimal Surfaces in $\mathbb{R}^3$
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866916076955107328 |
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| author | Yol, Ramazan |
| author_facet | Yol, Ramazan |
| contents | It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes with varying angle. We will study the limit of such surfaces when the angle converges to 0. In many cases, these limits are simpler than the original surface, and can be used in conjunction with the implicit function theorem to give new existence proofs of the original surfaces with small dihedral angle. This approach has led to the discovery of new minimal surfaces as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13473 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dihedralization of Minimal Surfaces in $\mathbb{R}^3$ Yol, Ramazan Differential Geometry 53A10 It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes with varying angle. We will study the limit of such surfaces when the angle converges to 0. In many cases, these limits are simpler than the original surface, and can be used in conjunction with the implicit function theorem to give new existence proofs of the original surfaces with small dihedral angle. This approach has led to the discovery of new minimal surfaces as well. |
| title | Dihedralization of Minimal Surfaces in $\mathbb{R}^3$ |
| topic | Differential Geometry 53A10 |
| url | https://arxiv.org/abs/2112.13473 |