Length functions in Teichm\'uller and anti de Sitter geometry
| Autor: | Mazzoli, Filippo, Viaggi, Gabriele |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Forum Math. Sigma 11, 2023, Paper No. e101 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/fms.2023.100 |
| Popis: | We establish a link between the behavior of length functions on Teichm\"uller 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 Teichm\"uller 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. Comment: 39 pages. Comments are welcome! |
| Databáze: | arXiv |
| Externí odkaz: |
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