  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.
