# Existence of CMC Cauchy surfaces and spacetime splitting

## TL;DR

This paper reviews the existence of constant mean curvature spacelike hypersurfaces in cosmology and explores their connection to spacetime splitting, highlighting key theoretical results and open questions.

## Contribution

It provides a comprehensive review of conditions for existence and nonexistence of CMC hypersurfaces and discusses their implications for spacetime splitting in general relativity.

## Key findings

- Summarizes known results on CMC hypersurfaces in cosmological spacetimes.
- Discusses the relationship between CMC hypersurfaces and spacetime splitting.
- Highlights open problems and future directions in the field.

## Abstract

In this paper, we review results on the existence (and nonexistence) of constant mean curvature spacelike hypersurfaces in the cosmological setting, and discuss the connection to the spacetime splittng problem. It is a pleasure to dedicate this paper to Robert Bartnik, who has made fundamental contributions to this area.