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Remarks on the Existence of CMC Cauchy Surfaces
Book chapter

Remarks on the Existence of CMC Cauchy Surfaces

Gregory J. Galloway and Eric Ling
Developments in Lorentzian Geometry, pp.93-104
Springer Proceedings in Mathematics & Statistics, Springer International Publishing
2022-10-07
DOI: https://doi.org/10.1007/978-3-031-05379-5_6

Abstract

CMC Cosmological spacetimes Mean curvature
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.

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