Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911098249150464 |
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| author | Chu, Adrian Chun-Pong |
| author_facet | Chu, Adrian Chun-Pong |
| contents | We describe some topological structure in the set of all surfaces with finitely many singularities in the 3-sphere.
As an application, we prove that every Riemannian 3-sphere of positive Ricci curvature contains, for every g, a genus g embedded minimal surface with area at most twice the first Simon-Smith width of the ambient 3-sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature Chu, Adrian Chun-Pong Differential Geometry Analysis of PDEs Geometric Topology We describe some topological structure in the set of all surfaces with finitely many singularities in the 3-sphere. As an application, we prove that every Riemannian 3-sphere of positive Ricci curvature contains, for every g, a genus g embedded minimal surface with area at most twice the first Simon-Smith width of the ambient 3-sphere. |
| title | Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature |
| topic | Differential Geometry Analysis of PDEs Geometric Topology |
| url | https://arxiv.org/abs/2508.06019 |