Existence of 5 minimal tori in 3-spheres of positive Ricci curvature
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918108240805888 |
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| author | Chu, Adrian Chun-Pong Li, Yangyang |
| author_facet | Chu, Adrian Chun-Pong Li, Yangyang |
| contents | In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5 embedded minimal tori. We confirm this conjecture for 3-spheres of positive Ricci curvature. While our proof uses min-max theory, the underlying heuristics are largely inspired by mean curvature flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of 5 minimal tori in 3-spheres of positive Ricci curvature Chu, Adrian Chun-Pong Li, Yangyang Differential Geometry Analysis of PDEs Geometric Topology In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5 embedded minimal tori. We confirm this conjecture for 3-spheres of positive Ricci curvature. While our proof uses min-max theory, the underlying heuristics are largely inspired by mean curvature flow. |
| title | Existence of 5 minimal tori in 3-spheres of positive Ricci curvature |
| topic | Differential Geometry Analysis of PDEs Geometric Topology |
| url | https://arxiv.org/abs/2409.09315 |