Degeneration of globally hyperbolic maximal anti-de Sitter structures along rays

Using the parameterisation of the deformation space of GHMC anti-de Sitter structures on $S \times \mathbb{R}$ by the cotangent bundle of the Teichmüller space of a closed surface $S$, we study how some geometric quantities, such as the Lorentzian Hausdorff dimension of the limit set, the width of the convex core and the Hölder exponent, degenerate along rays of cotangent vectors.

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Received 16 November 2017

Accepted 12 January 2020

Published 26 April 2023