Length functions in Teichmüller and anti de Sitter geometry
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914625133477888 |
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| author | Mazzoli, Filippo Viaggi, Gabriele |
| author_facet | Mazzoli, Filippo Viaggi, Gabriele |
| contents | We establish a link between the behavior of length functions on Teichmüller space and the geometry of certain anti de Sitter 3-manifolds. As an application, we give new purely anti de Sitter proofs of results of Teichmüller theory such as (strict) convexity of length functions along shear paths and geometric bounds on their second variation along earthquakes. Along the way, we provide shear-bend coordinates for Mess' anti de Sitter 3-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11106 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Length functions in Teichmüller and anti de Sitter geometry Mazzoli, Filippo Viaggi, Gabriele Geometric Topology Differential Geometry 53C50, 57M50, 57K20 We establish a link between the behavior of length functions on Teichmüller space and the geometry of certain anti de Sitter 3-manifolds. As an application, we give new purely anti de Sitter proofs of results of Teichmüller theory such as (strict) convexity of length functions along shear paths and geometric bounds on their second variation along earthquakes. Along the way, we provide shear-bend coordinates for Mess' anti de Sitter 3-manifolds. |
| title | Length functions in Teichmüller and anti de Sitter geometry |
| topic | Geometric Topology Differential Geometry 53C50, 57M50, 57K20 |
| url | https://arxiv.org/abs/2212.11106 |