  Let $M$ be a globally hyperbolic maximal compact $3$-dimensional spacetime
locally modelled on Minkowski, anti-de Sitter or de Sitter space. It is well
known that $M$ admits a unique foliation by constant mean curvature surfaces.
In this paper we extend this result to singular spacetimes with particles (cone
singularities of angles less than $\pi$ along time-like geodesics).
