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

Abstract

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 $S$, 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 quadratic differentials.

arXiv comment22 pages. To appear in Comm. Anal. Geom