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

2013/03/29 by Boubacar Diallo, Diallo, Boubacar · 3 citations
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1303.7406

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.

Cited by

• Group actions and scattering problems in Teichmüller theory
• Volume functions and boundary data of 3-dimensional hyperbolic manifolds
• On the Weyl problem for complete surfaces in the hyperbolic and anti-de Sitter spaces

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