Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910664391393280 |
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| author | Choudhury, Diptaishik Mazzoli, Filippo Seppi, Andrea |
| author_facet | Choudhury, Diptaishik Mazzoli, Filippo Seppi, Andrea |
| contents | Even though it is known that there exist quasi-Fuchsian hyperbolic three-manifolds that do not admit any monotone foliation by constant mean curvature (CMC) surfaces, a conjecture due to Thurston asserts the existence of CMC foliations for all almost-Fuchsian manifolds, namely those quasi-Fuchsian manifolds that contain a closed minimal surface with principal curvatures in (-1,1). In this paper we prove that there exists a (unique) monotone CMC foliation for all quasi-Fuchsian manifolds that lie in a sufficiently small neighborhood of the Fuchsian locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05736 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces Choudhury, Diptaishik Mazzoli, Filippo Seppi, Andrea Differential Geometry Geometric Topology Even though it is known that there exist quasi-Fuchsian hyperbolic three-manifolds that do not admit any monotone foliation by constant mean curvature (CMC) surfaces, a conjecture due to Thurston asserts the existence of CMC foliations for all almost-Fuchsian manifolds, namely those quasi-Fuchsian manifolds that contain a closed minimal surface with principal curvatures in (-1,1). In this paper we prove that there exists a (unique) monotone CMC foliation for all quasi-Fuchsian manifolds that lie in a sufficiently small neighborhood of the Fuchsian locus. |
| title | Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2204.05736 |