Constant mean curvature foliations of globally hyperbolic spacetimes locally modelled on $AdS_3$

Abstract

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 $τ$, such that every fiber $τ^{-1}(t)$ is a spacelike surface with constant mean curvature $t$.