Existence of four minimal spheres in $S^3$ with a bumpy metric
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929387528519680 |
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| author | Wang, Zhichao Zhou, Xin |
| author_facet | Wang, Zhichao Zhou, Xin |
| contents | We prove that in the three dimensional sphere with a bumpy metric or a metric with positive Ricci curvature, there exist at least four distinct embedded minimal two-spheres. This confirms a conjecture of S. T. Yau in 1982 for bumpy metrics and metrics with positive Ricci curvature. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08755 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence of four minimal spheres in $S^3$ with a bumpy metric Wang, Zhichao Zhou, Xin Differential Geometry Analysis of PDEs Geometric Topology We prove that in the three dimensional sphere with a bumpy metric or a metric with positive Ricci curvature, there exist at least four distinct embedded minimal two-spheres. This confirms a conjecture of S. T. Yau in 1982 for bumpy metrics and metrics with positive Ricci curvature. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory. |
| title | Existence of four minimal spheres in $S^3$ with a bumpy metric |
| topic | Differential Geometry Analysis of PDEs Geometric Topology |
| url | https://arxiv.org/abs/2305.08755 |