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arXiv · 2212.11106

Length functions in Teichm\"uller and anti de Sitter geometry

Filippo Mazzoli·Gabriele Viaggi
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Abstract

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.

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Filippo Mazzoli, Gabriele Viaggi. 2022-12-21. Length functions in Teichm\"uller and anti de Sitter geometry. https://doi.org/10.1017/fms.2023.100

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