, Volume 222, Issue 3, pp 533-567

On Long-Time Evolution in General Relativity¶and Geometrization of 3-Manifolds

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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.

Received: 21 August 2000 / Accepted: 28 May 2001