Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 1

CMC foliations of open spacetimes asymptotic to open Robertson–Walker spacetimes

Pages: 269 – 347

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n1.a8


Claus Gerhardt (Ruprecht-Karls-Universität, Institut für Angewandte Mathematik, Heidelberg, Germany)


We consider open globally hyperbolic spacetimes $N$ of dimension $n + 1, n \geq 3$, which are spatially asymptotic to a Robertson–Walker spacetime or an open Friedmann universe with spatial curvature $\tilde{\kappa} = 0, -1$ and prove, under reasonable assumptions, that there exists a unique foliation by spacelike hypersurfaces of constant mean curvature and that the mean curvature function $\tau$ is a smooth time function if $N$ is smooth. Moreover, among the Friedmann universes which satisfy the necessary conditions are those that reflect the present assumptions of the development of the universe.


Lorentzian manifold, mass, cosmological spacetime, general relativity, inverse mean curvature flow, ARW spacetimes

2010 Mathematics Subject Classification

35J60, 53C21, 53C44, 53C50, 58J05

Received 6 March 2020

Accepted 25 August 2020

Published 11 April 2021