On the existence of minimal Heegaard surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866917112537153536 |
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| author | Ketover, Daniel Liokumovich, Yevgeny Song, Antoine |
| author_facet | Ketover, Daniel Liokumovich, Yevgeny Song, Antoine |
| contents | Let $H$ be a strongly irreducible Heegaard surface in a closed oriented Riemannian $3$-manifold. We prove that $H$ is either isotopic to a minimal surface of index at most one or isotopic to the boundary of a tubular neighborhood about a non-orientable minimal surface with a vertical handle attached. This confirms a long-standing conjecture of J. Pitts and J.H. Rubinstein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_07161 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the existence of minimal Heegaard surfaces Ketover, Daniel Liokumovich, Yevgeny Song, Antoine Differential Geometry Geometric Topology Let $H$ be a strongly irreducible Heegaard surface in a closed oriented Riemannian $3$-manifold. We prove that $H$ is either isotopic to a minimal surface of index at most one or isotopic to the boundary of a tubular neighborhood about a non-orientable minimal surface with a vertical handle attached. This confirms a long-standing conjecture of J. Pitts and J.H. Rubinstein. |
| title | On the existence of minimal Heegaard surfaces |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/1911.07161 |