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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On Non-hyperbolic Quasi-convex Spaces
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by Rafael Oswaldo Ruggiero PDF
Trans. Amer. Math. Soc. 350 (1998), 665-687 Request permission

Abstract:

We show that if the universal covering of a compact Riemannian manifold with no conjugate points is a quasi-convex metric space then the following assertion holds: Either the universal covering of the manifold is a hyperbolic geodesic space or it contains a quasi-isometric immersion of $Z\times Z$.
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Additional Information
  • Rafael Oswaldo Ruggiero
  • Affiliation: Pontificia Universidade Católica do Rio de Janeiro, PUC-Rio, Dep. de Matemática, Rua Marqués de São Vicente 225, Gávea, Rio de Janeiro, Brasil
  • MR Author ID: 313673
  • Received by editor(s): April 25, 1994
  • Received by editor(s) in revised form: April 12, 1996
  • Additional Notes: Partially supported by CNPq of Brazilian Government
    The present paper was developed while the author was visiting at the École Normale Supérieure in Lyon from 09/93 to 08/94
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 665-687
  • MSC (1991): Primary 53C23; Secondary 53C20, 53C22, 53C40
  • DOI: https://doi.org/10.1090/S0002-9947-98-02075-3
  • MathSciNet review: 1451615