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ON LONG-TIME EVOLUTION IN GENERAL RELATIVITY AND GEOMETRIZATION OF 3-MANIFOLDS
 

Summary: ON LONG-TIME EVOLUTION IN GENERAL RELATIVITY AND
GEOMETRIZATION OF 3-MANIFOLDS
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 Space-Times. 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 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.
0. Introduction.
In this paper, we describe certain relations between the vacuum Einstein evolution equations
in general relativity and the geometrization of 3-manifolds. In its simplest terms, these relations
arise by analysing the long-time asymptotic behavior of natural space-like hypersurfaces   ; di eo-

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics