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

Thierry Barbot (1) , François Béguin (2) , Abdelghani Zeghib (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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 $t$.

Mots clés: CMC time function Globally hyperbolic spacetime anti-de Sitter

Domaines: Géométrie métrique [math.MG]

Thierry Barbot, François Béguin, Abdelghani Zeghib. Constant mean curvature foliations of globally hyperbolic spacetimes locally modelled on $AdS_3$. Geom. Ded., 2007, 126 (1), pp.71--129. ⟨hal-00003473⟩