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

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

2000-06-12

arxiv.org/abs/gr-qc/0006042v1

Commun.Math.Phys. 222 (2001) 533-567

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36pp

Scientific paper

10.1007/s002200100527

We describe some relations between the long-time asymptotic behavior of the vacuum Einstein evolution equations and the geometrization of 3-manifolds. These relations are expressed in terms of evolution of CMC hypersurfaces in the vacuum space-time.Some results are also obtained on the singularity avoidance of CMC foliations. In addition, the paper describes a number of open problems relating these two areas.

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