Volumes, courbure de Ricci et convergence des variétés

Sylvestre Gallot

Séminaire Bourbaki (1997-1998)

  • Volume: 40, page 7-32
  • ISSN: 0303-1179

How to cite


Gallot, Sylvestre. "Volumes, courbure de Ricci et convergence des variétés." Séminaire Bourbaki 40 (1997-1998): 7-32. <http://eudml.org/doc/110254>.

author = {Gallot, Sylvestre},
journal = {Séminaire Bourbaki},
keywords = {volume; diameter; Ricci curvature; Hausdorff distance; rigidity; splitting; regularity},
language = {fre},
pages = {7-32},
publisher = {Société Mathématique de France},
title = {Volumes, courbure de Ricci et convergence des variétés},
url = {http://eudml.org/doc/110254},
volume = {40},
year = {1997-1998},

AU - Gallot, Sylvestre
TI - Volumes, courbure de Ricci et convergence des variétés
JO - Séminaire Bourbaki
PY - 1997-1998
PB - Société Mathématique de France
VL - 40
SP - 7
EP - 32
LA - fre
KW - volume; diameter; Ricci curvature; Hausdorff distance; rigidity; splitting; regularity
UR - http://eudml.org/doc/110254
ER -


  1. [A-C] M. Anderson, J. Cheeger - Cα-compactness for manifolds with Ricci curvature and injectivity radius bounded below, Journ. Diff. Geom.35 (1992), 265-281. Zbl0774.53021
  2. [A-G] U. Abresch, D. Gromoll - On complete manifolds with nonnegative Ricci curvature, Journ. A.M.S. V.3 (1990), 355-374. Zbl0704.53032MR1030656
  3. [An1] M.T. Anderson - Metrics of Positive Ricci Curvature with Large Diameter, Manuscripta Math.68 (1990), 405-415. Zbl0711.53036MR1068264
  4. [An2] M.T. Anderson - Hausdorff perturbations of Ricci flat manifolds and the splitting theorem, Duke Math J.68 (1992), 67-82. Zbl0767.53029MR1185818
  5. [An3] M.T. Anderson - Convergence and rigidity of metrics under Ricci curvature bounds, Invent. Math102 (1990), 429-445. Zbl0711.53038MR1074481
  6. [B-C] R. Bishop, R. Crittenden - Geometry of Manifolds, Academic Press (1964). Zbl0132.16003MR169148
  7. [Be] M. Berger - Riemannian geometry during the second half of the century, preprint. 
  8. [B-I1] D. Burago, S. Ivanov - Riemannian tori without conjugate points are flat, Geom. and Funct. An.4 (1994), 259-269. Zbl0808.53038MR1274115
  9. [B-12] D. Burago, S. Ivanov - On asymptotic volume of Tori, Geom. and Funct. An.5 (1995), 800-808. Zbl0846.53043MR1354290
  10. [B-K] P. Buser, H. Karcher - Gromov's almost flat manifolds, Astérisque81 (1981), Soc. Math. France. Zbl0459.53031MR619537
  11. [Ch] J. Cheeger - Finiteness theorems for Riemannian manifolds, Am. J. of Math.92 (1970), 61-74. Zbl0194.52902MR263092
  12. [Ch-Co1] J. Cheeger, T.H. Colding - Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math.144 (1996), 189-237. Zbl0865.53037MR1405949
  13. [Ch-Co2] J. Cheeger, T.H. Colding - On the Structure of Spaces with Ricci curvature Bounded BelowI, J. Diff. Geom.46 (1997), 406-480. Zbl0902.53034MR1484888
  14. [Ch-Co3] J. Cheeger, T.H. Colding - On the Structure of Spaces with Ricci curvature Bounded Below II and III, annoncés. Zbl1027.53042
  15. [Ch-G1] J. Cheeger, D. Gromoll - The splitting theorem for manifolds of nonnegative Ricci curvature, Journ. Diff. Geom.6 (1971), 119-128. Zbl0223.53033MR303460
  16. [Ch-Gv] J. Cheeger, M. Gromov - Collapsing Riemannian manifolds while keeping their curvature bounded, II, J. Diff. Geom.31 (1990), 269-298. Zbl0727.53043MR1064875
  17. [Co1] T.H. Colding - Shape of manifolds with positive Ricci curvature, Invent. Math.124 (1996), 175-191. Zbl0871.53027MR1369414
  18. [Co2] T.H. Colding - Large manifolds with positive Ricci curvature, Invent. Math.124 (1996), 193-214. Zbl0871.53028MR1369415
  19. [Co3] T.H. Colding - Ricci curvature and volume convergence, Ann. of Math.145 (1997), 477-501. Zbl0879.53030MR1454700
  20. [C-Y] S.Y. Cheng, S.T. Yau - Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math.28 (1975), 333-354. Zbl0312.53031MR385749
  21. [F-Y] K. Fukaya, T. Yamaguchi - The fundamental groups of almost nonnegatively curved manifolds, Ann. of Math.136 (1992), 253-333. Zbl0770.53028MR1185120
  22. [Fu1] K. Fukaya - Collapsing Riemannian manifolds and eigenvalues of the Laplace operator, Inv. Math.87 (1987), 517-547. Zbl0589.58034MR874035
  23. [Fu2] K. Fukaya - Theory of convergence for Riemannian orbifolds, Japan. J. Math.12 (1986), 121-160. Zbl0654.53044MR914311
  24. [Ga] S. Gallot - A Sobolev inequality and some geometric applications, Actes du colloque de Kyoto (1981), Kaigai Publications, 45-55 (1983). 
  25. [Ge] R.E. Greene - Homotopy Finiteness theorems and Helly's theorem, J. Geom. Anal.4 (1994), 317-325. Zbl0803.53027MR1294330
  26. [G-L-P] M. Gromov, J. Lafontaine, P. Pansu - Structures métriques pour les variétés riemanniennes, Textes Mathématiques n° 1, Cedic - Nathan (1981). Zbl0509.53034MR682063
  27. [G-P] K. Grove, P. Petersen - A radius sphere theorem, Inventiones Math.112 (1993), 577-583. Zbl0801.53029MR1218324
  28. [G-P-W] K. Grove, P. Petersen, J.Y. Wu - Geometric finiteness theorems via controlled topology, Inv. Math.99 (1990), 205-213 et 104 (1991), 221-222. Zbl0747.53033MR1029396
  29. [Gv1] M. Gromov - Paul Levy's isoperimetric inequality, Prépublications de l'I.H.E.S. (1980). 
  30. [Ka] A. Katsuda - Gromov's convergence theorem and its applications, Nagoya Math. Journ.100 (1985), 11-48. Zbl0587.53043MR818156
  31. [Lo] J. Lohkamp - Manifolds of negative Ricci-curvature, Ann. of Math.140 (1994), 655-683. Zbl0824.53033MR1307899
  32. [O-S-Y] Y. Otsu, K. Shiohama, T. Yamaguchi - A new version of the differentiable sphere theorem, Invent. Math.98 (1989), 219-228. Zbl0688.53016MR1016261
  33. [Pan] P. Pansu - Volume, courbure et entropie (d'après G. Besson, G. Courtois et S. Gallot), Sém. Bourbaki, Nov. 1996, Exp. n° 823, Astérisque245 (1997), 83-103. Zbl1083.53502MR1627108
  34. [Pau] M. Paun - Thèse de l'Université Joseph Fourier, Grenoble. 
  35. [Per1] G. Perelman - Manifolds of Positive Ricci Curvature with almost maximal volume, Journ of the A.M.S.7 (1994), 299-305. Zbl0799.53050MR1231690
  36. [Per2] G. Perelman - Alexandrov's spaces with curvature bounded below II, preprint. MR1403952
  37. [Per3] G. Perelman - Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers, preprint. MR1452872
  38. [Pet] S. Peters - Convergence of Riemannian manifolds, Compositio Math.62 (1987), 3-16. Zbl0618.53036MR892147
  39. [Sh] K. Shiohama - A sphere theorem for manifolds of positive Ricci curvature, Trans. A.M.S.257 (1983), 811-819. Zbl0518.53047MR682734
  40. [Ya] T. Yamaguchi - Manifolds of almost nonnegative Ricci curvature, Journ. Diff. Geom.28 (1988), 157-167. Zbl0658.53036MR950560

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