 
Summary: ON LONGTIME EVOLUTION IN GENERAL RELATIVITY AND
GEOMETRIZATION OF 3MANIFOLDS
MICHAEL T. ANDERSON
Contents
0. Introduction. 1
1. Background and Preliminary Results. 7
2. Curvature Estimates on CMC Surfaces. 12
3. Asymptotics of Future Complete SpaceTimes. 17
4. The Future Boundary of MF in M. 28
5. Remarks on the Curvature Assumption. 32
References 33
Abstract. This paper introduces relations between the longtime asymptotic behavior of Einstein
vacuum spacetimes and the geometrization of 3manifolds 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 3manifold geometries. The CheegerGromov theory is introduced in this
context, and a number of open problems are considered from this viewpoint.
0. Introduction.
In this paper, we describe certain relations between the vacuum Einstein evolution equations
in general relativity and the geometrization of 3manifolds. In its simplest terms, these relations
arise by analysing the longtime asymptotic behavior of natural spacelike hypersurfaces ; dieo
