  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.
