Length functions in Teichmüller and anti-de Sitter geometry
Length functions in Teichmüller and anti-de Sitter geometry
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 …