Communications in Mathematical Physics

, Volume 222, Issue 3, pp 533–567

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

  • Michael T. Anderson

DOI: 10.1007/s002200100527

Cite this article as:
Anderson, M. Commun. Math. Phys. (2001) 222: 533. doi:10.1007/s002200100527

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michael T. Anderson
    • 1
  1. 1.Department of Mathematics, S.U.N.Y. at Stony Brook, Stony Brook, NY 11794-3651, USA.¶E-mail: anderson@math.sunysb.eduUS

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