Journal of Differential Geometry

On the structure of spaces with Ricci curvature bounded below. II

Jeff Cheeger and Tobias H. Colding

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 54, Number 1 (2000), 13-35.

Dates
First available in Project Euclid: 24 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214342145

Digital Object Identifier
doi:10.4310/jdg/1214342145

Mathematical Reviews number (MathSciNet)
MR1815410

Zentralblatt MATH identifier
1027.53042

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35] 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Citation

Cheeger, Jeff; Colding, Tobias H. On the structure of spaces with Ricci curvature bounded below. II. J. Differential Geom. 54 (2000), no. 1, 13--35. doi:10.4310/jdg/1214342145. https://projecteuclid.org/euclid.jdg/1214342145


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References

  • [1] M. T. Anderson, Hausdorff perturbations of Ricci flat manifolds and the splitting theorem, Duke Math. J. 68 (1992) 67-82.
  • [2] J. Cheeger and T. H. Colding, Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below, C.R. Acad. Sci. Paris t. 320, Ser. 1 (1995) 353-357.
  • [3] J. Cheeger and T. H. Colding, Lower bounds on the Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996) 189-237.
  • [4] J. Cheeger and T. H. Colding, On the structure of spaces with Ricci curvature bounded below. I, J. Differential Geom. 46 (1997) 406-480.
  • [5] J. Cheeger and T. H. Colding, On the structure of spaces with Ricci curvature bounded below. Ill, J. Differential Geom. 54 (2000) 37-74.
  • [6] J. Cheeger, T. H. Colding and G. Tian, Constraints on singularities under Ricci curvature bounds, C.R. Acad. Sci. Paris, t. 324, Série 1 (1997) 645-649.
  • [7] J. Cheeger, T. H. Colding and G. Tian, On the singularities of spaces with bounded Ricci curvature, Preprint.
  • [8] S. Y. Cheng and S.-T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975) 333-354.
  • [9] T. H. Colding, Stability and Ricci curvature, C.R. Acad. Sci. Paris, t. 320, Ser. 1 (1995) 1343-1347.
  • [10] T. H. Colding, Shape of manifolds with positive Ricci curvature, Invent. Math. 124 (1996) 175-191.
  • [11]T. H. Colding, Large manifolds with positive Ricci curvature, Invent. Math. 124 (1996) 193-214.
  • [12] T. H. Colding, Ricci curvature and volume convergence, Ann. of Math. 145 (1997) 477-501.
  • [13] T. H. Colding and W. P. Minicozzi II, Harmonic functions with polynomial growth, J. Differential Geom. 46 (1997) 1-77.
  • [14] H. Fédérer, Geometric measure theory, Springer, Berlin-New York, 1969.
  • [15] K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of the Laplace operator, Invent. Math. 87 (1987) 517-547.
  • [16] K. Fukaya and T. Yamaguchi, Isometry group of singular spaces, Math. Z., 216 (1994) 31-44.
  • [17] A. Gleason, Groups without small subgroups, Ann. of Math. 56 (1952) 193-212.
  • [18] M. Gromov, J. Lafontaine and P. Pansu, Structures métriques pour les varieties riemanniennes, Cedic/Fernand Nathan, Paris, 1981.
  • [19] M. Gromov, Paul-Levy's isoperimetric inequality, 1980, Preprint.
  • [20] M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Etudes Sci. Publ. Math. 53 (1981) 53-73.
  • [21] H. Yamabe, A generalization of a theorem of Gleason, Ann. of Math. 58 (1953) 351-364.

See also

  • Part I: Jeff Cheeger, Tobias H. Colding. On the structure of spaces with Ricci curvature bounded below. I. J. Differential Geom., Volume 46, Number 3, (1997), 406--480.
  • Part III: Jeff Cheeger, Tobias H. Colding. On the structure of spaces with Ricci curvature bounded below. III. J. Differential Geom., Volume 54, Number 1, (2000), 37--74.