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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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Lipschitz precompactness for closed negatively curved manifolds
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by Igor Belegradek PDF
Proc. Amer. Math. Soc. 127 (1999), 1201-1208 Request permission

Abstract:

We prove that, given a integer $n\ge 3$ and a group $\pi$, the class of closed Riemannian $n$-manifolds of uniformly bounded negative sectional curvatures and with fundamental groups isomorphic to $\pi$ is precompact in the Lipschitz topology. In particular, the class breaks into finitely many diffeomorphism types.
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Additional Information
  • Igor Belegradek
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • Address at time of publication: Department of Mathematics and Statistics, McMaster University, 1280 Main St. West, Hamilton, Ontario, Canada L8S 4K1
  • MR Author ID: 340900
  • Email: igorb@math.umd.edu, belegi@icarus.math.mcmaster.ca
  • Received by editor(s): July 30, 1997
  • Communicated by: Christopher Croke
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1201-1208
  • MSC (1991): Primary 53C20, 53C23; Secondary 20F32, 57R55
  • DOI: https://doi.org/10.1090/S0002-9939-99-04654-7
  • MathSciNet review: 1476116