Geometrization of 3-manifolds via the Ricci flow

Notices of the American Mathematical Society

Volumn 51, Issue 2, 2004, Pages 184-193

  Anderson, Michael T ^a  

^a Stony Brook University   (United States)

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[No Author keywords available]

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EID: 14844304802     PISSN: 00029920     EISSN: 10889477     Source Type: Journal    
DOI: None     Document Type: Review

References (20)

1. M. ANDERSON, Scalar curvature and geometrization conjectures for 3-manifolds, in Comparison Geometry (Berkeley 1993-94), MSRI Publications, vol. 30, 1997, pp. 49-82.
2. _, Scalar curvature and the existence of geometric structures on 3-manifolds. I, J. Reine Angew. Math. 553 (2002), 125-182.
3. L. ANDERSSON, The global existence problem in general relativity, preprint, 1999, gr-qc/9911032; to appear in 50 Years of the Cauchy Problem in General Relativity, P. T. Chruściel and H. Friedrich, eds.
4. H.-D. CAO and B. CHOW, Recent developments on the Ricci now, Bull. Amer. Math. Soc. (N.S.) 36 (1999), 59-74.
5. E. D'HOKER, String theory, in Quantum Fields and Strings: A Course for Mathematicians, Vol. 2, Amer. Math. Soc., Providence, RI, 1999.
6. M. GROMOV, Structures Métriques pour les Variétés Riemanniennes, Cedic/Fernand Nathan, Paris, 1981.
7. _, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 50 (1982), 5-100.
8. R. HAMILTON, Three manifolds of positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306.
9. _, The Harnack estimate for the Ricci flow, J. Differential Geom. 37 (1993), 225-243.
10. _, Formation of singularities in the Ricci flow, Surveys in Differential Geometry, Vol. 2, International Press, 1995, pp. 7-136.
11. _, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom. 7 (1999), 695-729.
12. T. IVEY, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993), 301-307.
13. B. KLEINER and J. LOTT, Ricci flow website: http:// www.math.lsa.umich. edu/research/ricciflow/ perelman.html.
14. J. MILNOR, Towards the Poincaré Conjecture and the classification of 3-manifolds, preprint, 2003; Notices Amer. Math. Soc. 50 (2003), 1226-1233.
15. G. PERELMAN, The entropy formula for the Ricci flow and its geometric applications, preprint, 2002, math.DG/0211159.
16. _, Ricci flow with surgery on three-manifolds, preprint, 2003, math.DG/0303109.
17. _, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint, 2003, math.DG/0307245.
18. W. THURSTON, The Geometry and Topology of Three-Manifolds, preprint, 1978, Princeton University, available online at http://www.msri.org/ publications/ books/gt3m;
19. and Three-Dimensional Geometry and Topology, Vol. 1, Princeton University Press, 1997.
20. _, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N. S.) 6 (1982), 357-381.