The Einstein flow, the σ-constant and the geometrization of 3-manifolds

Classical and Quantum Gravity

Volumn 16, Issue 11, 1999, Pages

  Fischer, Arthur E ^a   Moncrief, Vincent ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033239931     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/16/11/102     Document Type: Article

References (18)

1. Fischer A and Moncrief V 1994 Reducing Einstein's equations to an unconstrained Hamiltonian system on the cotangent bundle of Teichmüller space in Physics on Manifolds, Proc. of the Int. Coll. in Honour of Yvonne Choquet-Bruhat ed M Flato, R Kerner and A Lichnerowicz (Boston: Kluwer) pp 111-51
2. Fischer A and Moncrief V 1996 The structure of quantum conformal superspace Global Structure and Evolution in General Relativity, Proc. First Samos Meeting on Cosmology, Geometry and Relativity (Karlovassi, Samos, Greece, 5-7 September 1994) ed S Cotsakis and G W Gibbons (Berlin: Springer) pp 111-73
3. Fischer A and Moncrief V 1997 Hamiltonian reduction of Einstein's equations of general relativity Nucl. Phys. B (Proc. Suppl.) 57 142-61
4. Moncrief V 1989 Reduction of the Einstein equations in 2+1 dimensions to a Hamiltonian system over Teichmüller space J. Math. Phys. 30 2907-14
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6. Fischer A and Moncrief V 1999 The reduced Hamiltonian of general relativity and the σ-constant of conformal geometry Proc. 2nd Samos Meeting on Cosmology, Geometry and Relativity, Mathematical and Quantum Aspects of Relativity and Cosmology (Samos, 31 August-4 September, 1998) (Lecture Notes in Physics) ed S Cotsakis and G W Gibbons (New York: Springer)
7. Palais R and Terng C 1988 Critical point theory and submanifold geometry Lecture Notes in Mathematics, vol 1353 (New York: Springer)
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9. Choquet-Bruhat Y and York J 1980 The Cauchy Problem General Relativity and Gravitation: Volume 1 ed A Held (New York: Plenum)
10. Löbell F 1931 Beispele geschlossener drei-dimensionaler Clifford-Kleinsche Räume negativer Krümmung Ber. Verhandl. Sächs. Akad. Wiss. Leipzig, Math. Phys. Kl. 83 167-74
11. Eardley D, Isenberg J, Marsden J and Moncrief V 1986 Homothetic and conformal symmetries of solutions to Einstein's equations Commun. Math. Phys. 106 137-58
12. Andersson L and Moncrief V 2000 The global existence problem in general relativity, in preparation
13. Christodoulou D and Klainerman S 1993 The Global Nonlinear Stability of the Minkowski Space (Princeton, NJ: Princeton University Press)
14. Anderson M 1993 Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals Proc. Symp. on Pure Mathematics vol 54, part 3, pp 53-79
15. Thurston W 1997 Three-dimensional Geometry and Topology vol 1, ed S Levy (Princeton, NJ: Princeton University Press)
16. Hamilton R 1982 Three manifolds with positive Ricci curvature J. Diff. Geom. 17 255-306
17. Hamilton R 1999 Non-singular solutions of the Ricci flow on three-manifolds Commun. Anal. Geom. 7 695-729
18. Cao H and Chow B 1999 Recent developments on the Ricci flow Bull. Am. Math. Soc. 36 59-74