Constant mean curvature foliation of globally hyperbolic (2+1)-spacetimes with particles

Abstract

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).

39 pages

References in corpus (4)

• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Prescribing metrics on the boundary of AdS 3-manifolds
• Constant Gauss curvature foliations of AdS spacetimes with particles
• Constant mean curvature foliation of domains of dependence in $Ad{S}_3$