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arXiv · 1303.7406

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

Boubacar Diallo
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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 Teichm\"uller theory and earthquakes.

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Boubacar Diallo. 2013-03-29. Prescribing metrics on the boundary of convex cores of globally hyperbolic maximal compact AdS 3-manifolds. https://arxiv.org/abs/1303.7406

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