3.1 CMC foliations
Note that CMC foliations are unique in cosmological vacuum spacetimes. In the case of
vacuum T3-Gowdy, there is a CMC foliation exhausting the interval
[49
]. However,
in the case of S2 × S1 and S3 topology, the only general statements concerning foliations
are, as far as we are aware, the ones given in [16
]. It is natural to conjecture that if there is a
CMC Cauchy hypersurface in the S2 × S1 or S3 case, there is a CMC foliation exhausting the
interval
[66]. However, to the best of our knowledge there are no results to this
effect.