On long-time evolution in general relativity and geometrization of   3-manifolds
  We describe some relations between the long-time asymptotic behavior of the vacuum Einstein evolution equations and the geometrization of 3-manifolds. These relations are expressed in terms of evolution of CMC hypersurfaces in the vacuum space-time.Some results are also obtained on the singularity avoidance of CMC foliations. In addition, the paper describes a number of open problems relating these two areas. 
Michael T. Anderson (SUNY Stony Brook)