On long-time evolution in general relativity and geometrization of 3-manifolds

This paper introduces relations between the long-time asymptotic behavior of Einstein vacuum space-times and the geometrization of 3-manifolds envisioned by Thurston. The relations are obtained by analysing the asymptotic behavior of a CMC foliation by compact Cauchy surfaces and the induced curve of 3-manifold geometries. The Cheeger-Gromov theory is introduced in this context, and a number of open problems are considered from this viewpoint.