Prescribing metrics on the boundary of convex cores of globally hyperbolic maximal compact AdS 3-manifolds

Abstract

We consider globally hyperbolic maximal anti de Sitter 3-manifolds $M$ with a closed Cauchy surface $S$ of genus greater than one and prove that any pair of hyperbolic metrics on $S$ can be realized as the boundary metrics of the convex core of a maximal globally hyperbolic anti de Sitter 3-manifold structure on $M$. This answers the existence part of a question of Mess about the unique realization of such metrics. Our theorem has a nice formulation purely in terms of 2-dimensional Teichmüller theory and earthquakes.

arXiv comment17 pages, 5 figures. Part of my PhD thesis

References in corpus (2)

• Minimal stretch maps between hyperbolic surfaces
• Fixed points of compositions of earthquakes

Cited by in corpus (4)

• The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti de Sitter geometry
• On the Weyl problem for complete surfaces in the hyperbolic and anti-de Sitter spaces
• Group actions and scattering problems in Teichmüller theory
• Prescribing metrics on the boundary of AdS 3-manifolds