Constant mean curvature foliations of globally hyperbolic spacetimes   locally modelled on $AdS_3$
  We prove that any maximal globally hyperbolic spacetime locally modelled on the anti-de Sitter space of dimension 3, and admitting a closed Cauchy surface, admits a time function $\tau$, such that every fiber $\tau^{-1}(t)$ is a spacelike surface with constant mean curvature $t$. 
Thierry Barbot (UMPA-ENSL), Francois Beguin (LM-Orsay), Abdelghani   Zeghib (UMPA-ENSL)