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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the fundamental groups of manifolds with almost-nonnegative Ricci curvature
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by Guofang Wei PDF
Proc. Amer. Math. Soc. 110 (1990), 197-199 Request permission

Abstract:

We give an upper bound on the growth of ${\pi _1}\left ( M \right )$ for a class of manifolds $M$ with Ricci curvature ${\text {Ri}}{{\text {c}}_M} \geq - \varepsilon$, diameter $d\left ( M \right ) = 1$, and volume ${\text {vol}}\left ( M \right ) \geq \upsilon$.
References
  • Michael T. Anderson, Short geodesics and gravitational instantons, J. Differential Geom. 31 (1990), no. 1, 265–275. MR 1030673
  • M. Gromov, Synthetic geometry in Riemannian manifolds, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 415–419. MR 562635
  • —, Structures métriques pour les variétés Riemanniennes, Cedic Fernand-Nathan, Paris, 1981.
  • J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1–7. MR 232311
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 110 (1990), 197-199
  • MSC: Primary 53C20; Secondary 20F34, 22E40, 57M05, 57S20
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1021214-X
  • MathSciNet review: 1021214