Bounds on the fundamental group of a manifold with almost nonnegative Ricci curvature

Steven ROSENBERG; Deane YANG

doi:10.2969/jmsj/04620267

Steven ROSENBERG, Deane YANG

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 2 Pages 267-287

DOI https://doi.org/10.2969/jmsj/04620267

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Published: 1994 Received: July 06, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. T. Anderson, Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals, Differential Geometry: Riemannian geometry, (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., 54, Part 3, Amer. Math. Soc., Providence, RI, 1993, pp. 53-79.
2) P. Bérard, A lower bound for the least eigenvalue of Δ+V, Manuscripta Math., 69 (1990), 255-259.
3) P. Bérard, A note on Bochner type theorems for complete manifolds, Manuscripta Math., 69 (1990), 261-266.
4) C. B. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Sci. École Norm. Sup., 13 (1980), 419-435.
5) K. D. Elworthy and S. Rosenberg, Manifolds with wells of negative Ricci curvature, Invent. Math., 103 (1991), 471-495.
6) S. C. Ferry, Counting simple homotopy types in Gromov-Hausdorff space, preprint, 1991.
7) S. Gallot, Isoperimetric inequalities based on integral norms of Ricci curvature, Asterisque, 157-158 (1988), 191-216.
8) M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES., 53 (1981), 183-215.
9) M. Gromov, J. Lafontaine and P. Pansu, Structures métriques pour les variétés riemanniennes, Paris, Cedic, 1981.
10) E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup., 11 (1978), 451-470.
11) J. Milnor, A note on curvature and fundamental group, J. Differential Geometry, 2 (1968), 1-7.
12) J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure and Applied Math., 17 (1964), 101-134.
13) Z. Shen and G. Wei, On Riemannian manifolds of almost nonnegative curvature, Indiana Univ. Math. J., 40 (1991), no. 2, 551-565.
14) P. Petersen V., A finiteness theorem for metric spaces, J. Differential Geom., 31 (1990), 387-395.
15) G. Wei, On the fundamental groups of manifolds with almost nonnegative Ricci curvature, Proc. Amer. Math. Soc., 110 (1990), 197-199.
16) J.-Y. Wu, Complete manifolds with a little negative curvature, Amer. J. Math., 113 (1991), 567-572.
17) D. Yang, Convergence of Riemannian manifolds with integral bounds on curvature I, Ann. Sci. École Norm. Sup. (4), 25 (1992), no. 1, 77-105.

Right : [1] M. T. Anderson, Degeneration of metrics with bounded curvature and applications to critical metrics of Riemannian functionals, Differential Geometry: Riemannian geometry, (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., 54, Part 3, Amer. Math. Soc., Providence, RI, 1993, pp. 53-79.
[2] P. Bérard, A lower bound for the least eigenvalue of Δ+V, Manuscripta Math., 69 (1990), 255-259.
[3] P. Bérard, A note on Bochner type theorems for complete manifolds, Manuscripta Math., 69 (1990), 261-266.
[4] C. B. Croke, Some isoperimetric inequalities and eigenvalue estimates, Ann. Sci. École Norm. Sup., 13 (1980), 419-435.
[5] K. D. Elworthy and S. Rosenberg, Manifolds with wells of negative Ricci curvature, Invent. Math., 103 (1991), 471-495.
[6] S. C. Ferry, Counting simple homotopy types in Gromov-Hausdorff space, preprint, 1991.
[7] S. Gallot, Isoperimetric inequalities based on integral norms of Ricci curvature, Asterisque, 157-158 (1988), 191-216.
[8] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. IHES., 53 (1981), 183-215.
[9] M. Gromov, J. Lafontaine and P. Pansu, Structures métriques pour les variétés riemanniennes, Paris, Cedic, 1981.
[10] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup., 11 (1978), 451-470.
[11] J. Milnor, A note on curvature and fundamental group, J. Differential Geometry, 2 (1968), 1-7.
[12] J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure and Applied Math., 17 (1964), 101-134.
[13] Z. Shen and G. Wei, On Riemannian manifolds of almost nonnegative curvature, Indiana Univ. Math. J., 40 (1991), no. 2, 551-565.
[14] P. Petersen V., A finiteness theorem for metric spaces, J. Differential Geom., 31 (1990), 387-395.
[15] G. Wei, On the fundamental groups of manifolds with almost nonnegative Ricci curvature, Proc. Amer. Math. Soc., 110 (1990), 197-199.
[16] J. -Y. Wu, Complete manifolds with a little negative curvature, Amer. J. Math., 113 (1991), 567-572.
[17] D. Yang, Convergence of Riemannian manifolds with integral bounds on curvature I, Ann. Sci. École Norm. Sup. (4), 25 (1992), no. 1, 77-105.

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