Scalar curvature and the existence of geometric structures on 3-manifolds, I

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 553, 2002, Pages 125-182

  Anderson, Michael T ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036918681     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2002.096     Document Type: Article

References (39)

1. M. Anderson, Scalar curvature and geometrization conjectures for 3-manifolds, Comparison Geometry, MSRI Publ. 30 (1997), 49-82.
2. M. Anderson, Extrema of curvature functional on the space of metrics on 3-manifolds, Calc. Var. P.D.E. 5 (1997), 199-269.
3. M. Anderson, Extrema of curvature functionals on the space of metrics on 3-manifolds, II, Calc. Var. P.D.E. 12 (2001), 1-58.
4. M. Anderson, Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds, I, Geom. Funct. Anal. 9 (1999), 855-967.
5. M. Anderson, Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds, II, Geom. Funct. Anal. 11 (2001), 273-381
6. A. Besse, Einstein Manifolds, Ergeb. Math. 3. Folge 10, Springer Verlag, New York 1987.
7. J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded I, J. Diff. Geom. 23 (1986), 309-346.
8. J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded II, J. Diff. Geom. 32 (1990), 269-298.
9. K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimension, J. Diff. Geom. 25 (1987), 139-156.
10. S. Gallot, Isoperimetric inequalities based on integral norms of Ricci curvature, Astérisque 157-158 (1988), 191-217.
11. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of the Second Order, 2nd Ed., Springer Verlag, New York 1983.
12. M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Progr. Math. 152, Birkhäuser Verlag, Boston 1999.
13. M. Gromov, Volume and bounded cohomology, Publ. Math. I.H.E.S. 56 (1982), 5-100.
14. M. Gromov and H. Lawson, Jr., Spin and scalar curvature in the presence of a fundamental group, Ann. Math. 111 (1980), 209-230.
15. M. Gromov and H. Lawson, Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I.H.E.S. 58 (1983), 83-196.
16. R. Hamilton, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Geom. Anal. 7 (1999), 695-729.
17. W. Hayman, Subharmonic Functions, Academic Press, London 1976.
18. W. Jaco, Lectures on Three-Manifold Topology, Conf. Bd. Math. Sci. A.M.S. 43 (1980).
19. W. Jaco and P. Shalen, Seifert fibered spaces in 3-manifolds, Mem. A.M.S. 220 (1979).
20. H. Jacobowitz, Local isometric embeddings of surfaces into Euclidean four space, Indiana Univ. Math. J. 21 (1971), 249-254.
21. K. Johannson, Homotopy equivalence of 3-manifolds with boundaries, Springer Lect. Notes Math. 761 (1979).
22. M. Kneser, Geschlossene Flächen in dreidimensionale Mannifaltigkeiten, Jahresber. Deutsch. Math. Verein. 38 (1929), 248-260.
23. O. Kobayashi, Scalar curvature of a metric of unit volume, Math. Ann. 279 (1987), 253-265.
24. J. Milnor, A unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7.
25. G. Mostow, Quasiconformal mappings in n-space and the strong rigidity of hyperbolic space forms, Publ. Math. I.H.E.S. 34 (1968), 53-104.
26. P. Orlik, Seifert Manifolds, Springer Lect. Notes Math. 291 (1972).
27. G. Prasad, Strong rigidity of Q-rank 1 lattices, Invent. Math. 21 (1973), 255-286.
28. X. Rang, The limiting eta invariant of collapsed 3-manifolds, J. Diff. Geom. 37 (1993), 535-568.
29. R. Schoen, Conformal deformation of a metric to constant scalar curvature, J. Diff. Geom. 20 (1985), 479-495.
30. R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Springer Lect. Notes Math. 1365 (1987), 120-154.
31. R. Schoen and S.-T. You, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non negative scalar curvature, Ann. Math. 110 (1979), 127-142.
32. R. Schoen and S.-T. You, On the structure of manifolds with positive scalar curvature, Manuscr. Math. 29 (1979), 159-183.
33. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487.
34. T. Soma, The Gromov invariant of links, Invent. Math. 64 (1981), 445-454.
35. M. Spivak, A Comprehensive Introduction to Differential Geometry, V, Publish or Perish, Houston 1979.
36. W. Thurston, The Geometry and Topology of 3-Manifolds, preprint, Princeton 1979.
37. W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. A.M.S. 6 (1982), 357-381.
38. F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I, Invent. Math. 3 (1967), 308-333.
39. F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten II, Invent. Math. 4 (1967), 87-117.