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

摘要

Using the parameterisation of the deformation space of GHMC anti-de Sitter structures on S x R by the cotangent bundle of the Teichmuller 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 Holder exponent, degenerate along rays of cotangent vectors.