Remarks on the existence of CMC Cauchy surfaces
General Relativity and Quantum Cosmology
2021-11-12 v2 Differential Geometry
Abstract
As is well known, constant mean curvature (CMC) spacelike hypersurfaces play an important role in solving the Einstein equations, both in solving the contraints and the evolution equations. In this paper we review the CMC existence result obtained by the authors in [10] and consider some new existence results motivated by a conjecture of Dilts and Holst [8]. We also address some issues concerning the conformal structure of cosmological spacetimes.
Keywords
Cite
@article{arxiv.2104.02136,
title = {Remarks on the existence of CMC Cauchy surfaces},
author = {Gregory J. Galloway and Eric Ling},
journal= {arXiv preprint arXiv:2104.02136},
year = {2021}
}
Comments
13 pages; v2: minor corrections/clarifications. To appear in the Proceedings of the X International Meeting on Lorentzian Geometry