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 GHMC anti-de Sitter 3-manifolds.
Length functions in Teichmüller and anti-de Sitter geometry / Mazzoli, Filippo; Viaggi, Gabriele. - In: FORUM OF MATHEMATICS. SIGMA. - ISSN 2050-5094. - 11:(2023). [10.1017/fms.2023.100]
Length functions in Teichmüller and anti-de Sitter geometry
Viaggi, Gabriele
2023
Abstract
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 GHMC anti-de Sitter 3-manifolds.| File | Dimensione | Formato | |
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