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

## TL;DR

This paper extends the existence and uniqueness of constant mean curvature foliations to singular 3D spacetimes with particles, which have cone singularities along timelike geodesics, in Minkowski, anti-de Sitter, or de Sitter models.

## Contribution

It generalizes the classical foliation result to include singular spacetimes with particles, broadening the understanding of their geometric structure.

## Key findings

- Existence of CMC foliation in singular spacetimes with particles.
- Uniqueness of the foliation in these singular settings.
- Extension of classical results to include cone singularities.

## 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).