Remarks on the existence of CMC Cauchy surfaces

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.

13 pages; v2: minor corrections/clarifications. To appear in the Proceedings of the X International Meeting on Lorentzian Geometry

References in corpus (3)

• Initial data engineering
• Friedmann's Equations in All Dimensions and Chebyshev's Theorem
• When Do Spacetimes Have Constant Mean Curvature Slices?

Cited by in corpus (1)

• Conformal Rigidity from Focusing