The reduced Einstein equations and the conformal volume collapse of 3-manifolds

Classical and Quantum Gravity

Volumn 18, Issue 21, 2001, Pages 4493-4515

  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: 0035540091     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/18/21/308     Document Type: Article

References (29)

1. Anderson M 1993-94 Scalar curvature and geometrization conjectures for 3-manifolds Comparison Geometry (Berkeley, CA: University of California) Anderson M 1997 Math. Sci. Res. Inst. Publ. vol 30 (Cambridge: Cambridge University Press)
2. Anderson M 1993-94 Scalar curvature and geometrization conjectures for 3-manifolds Comparison Geometry (Berkeley, CA: University of California) Anderson M 1997 Math. Sci. Res. Inst. Publ. vol 30 (Cambridge: Cambridge University Press)
3. Anderson M 1999 Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds I Geom. Funct. Anal. 9 855-967
4. Andersson L and Moncrief V The global existence problem in general relativity, in preparation
5. Arnowitt R, Deser S and Misner C 1962 The dynamics of general relativity Gravitation: an Introduction to Current Research ed L Witten (New York: Wiley)
6. Choquet-Bruhat Y and York J 1980 The Cauchy problem Geneneral Relativity and Gravitation vol 1, ed A Held (New York: Plenum)
7. Christodoulou D and Klainerman S 1993 The Global Nonlinear Stability of the Minkowski Space (Princeton, NJ: Princeton University Press)
8. Fischer A and Marsden J 1975 Deformations of the scalar curvature Duke Math. J. 42 519-47
9. Fischer A and Moncrief V 1996 The structure of quantum conformal superspace Global Structure and Evolution in General Relativity ed S Cotsakis and G Gibbons (Berlin: Springer) pp 111-73
10. Fischer A and Moncrief V 1997 Hamiltonian reduction of Einstein's equations of general relativity Nucl. Phys. B (Proc. Suppl) 57 142-61
11. Fischer A and Moncrief V 1999 The Einstein flow, the σ-constant and geometrization of 3-manifolds Class. Quantum Grav. 16 L79-87
12. Fischer A and Moncrief V 2000 The reduced Hamiltonian of general relativity and the σ-constant of conformal geometry Proc. 2nd Samos Meeting on Cosmology, Geometry and Relativity ed S Cotsakis and G W Gibbons (New York: Springer)
13. Fischer A and Moncrief V 2000 Hamiltonian reduction, the Einstein flow and collapse of 3-manifolds Nucl. Phys. B (Proc. Suppl.) 88 83-102
14. Fischer A and Moncrief V 2002 Conformal volume collapse of spatially compact Bianchi models under the reduced Einstein flow, to appear
15. Fischer A and Moncrief V 2002 Conformal volume collapse of 3-manifolds and the reduced Einstein flow Geometry, Dynamics and Mechanics: 60th Birthday Volume for J E Marsden ed P Holmes, P K Newton and A Weinstein (Berlin: Springer) pp 1-60 to appear
16. Gromov M 1978 Almost flat manifolds J. Diff. Geom. 13 231-41
17. Gromov M 1982 Volume and bounded cohomology Publ. Math. IHES 56 5-99
18. Lafontaine J 1983 Modules de structures conformes plates et cohomologie de groupes discrets C. R. Acad. Sci., Paris 1 297 655-8
19. O'Neill B 1983 Semi-Riemannian Geometry with Applications to Relativity (New York: Academic)
20. Ringström H 2000 Curvature blow up in Bianchi V III and IX vacuum spacetimes Class. Quantum Grav. 17 713-31 (Ringström H 1999 Preprint gr-qc/9911115)
21. Ringström H 2000 Curvature blow up in Bianchi V III and IX vacuum spacetimes Class. Quantum Grav. 17 713-31 (Ringström H 1999 Preprint gr-qc/9911115)
22. Ringström H 2001 The future asymptotics of Bianchi VIII vacuum solutions Class. Quantum Grav. 18 3791-824 (Ringström H 2001 Preprint gr-qc/0103107)
23. Ringström H 2001 The future asymptotics of Bianchi VIII vacuum solutions Class. Quantum Grav. 18 3791-824 (Ringström H 2001 Preprint gr-qc/0103107)
24. Tanimoto M, Koike T and Hosoya A 1994 Compact homogeneous universes J. Math. Phys. 35 4855-88
25. Tanimoto M, Koike T and Hosoya A 1997 Dynamics of compact homogeneous universes J. Math. Phys. 38 350-68
26. Tanimoto M, Koike T and Hosoya A 1997 Hamiltonian structures for compact homogeneous universes J. Math. Phys. 38 6560-77
27. Thurston W 1997 Three-Dimensional Geometry and Topology vol 1, ed S Levy (Princeton, NJ: Princeton University Press)
28. Wainwright J and Ellis G F R 1997 Dynamical Systems in Cosmology (Cambridge: Cambridge University Press)
29. Wolf J 1972 Spaces of Constant Curvature 2nd edn (Berkeley, CA: Publish or Perish)