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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Gromov hyperbolicity of the $j_G$ and ${\tilde \jmath }_G$ metrics
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by Peter A. Hästö PDF
Proc. Amer. Math. Soc. 134 (2006), 1137-1142 Request permission

Abstract:

In this note it is shown that the ${\tilde \jmath }_G$ metric is always Gromov hyperbolic, but that the $j_G$ metric is Gromov hyperbolic if and only if $G$ has exactly one boundary point. As a corollary we get a new proof for the fact that the quasihyperbolic metric is Gromov hyperbolic in uniform domains.
References
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Additional Information
  • Peter A. Hästö
  • Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
  • Address at time of publication: Department of Mathematics and Statistics, P.O. Box 68, FIN-00014 University of Helsinki, Finland
  • Email: peter.hasto@helsinki.fi
  • Received by editor(s): March 3, 2004
  • Received by editor(s) in revised form: November 3, 2004
  • Published electronically: August 29, 2005
  • Additional Notes: The author was supported in part by a Gehring-Finland Post-doctoral Fellowship and by the Finnish Academy of Science and Letters.
  • Communicated by: Juha M. Heinonen
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 1137-1142
  • MSC (2000): Primary 30F45; Secondary 53C23, 30C99
  • DOI: https://doi.org/10.1090/S0002-9939-05-08053-6
  • MathSciNet review: 2196049