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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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Uniform approximation of metrics by graphs
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by Dmitri Burago and Sergei Ivanov PDF
Proc. Amer. Math. Soc. 143 (2015), 1241-1256 Request permission

Abstract:

We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one within a finite Gromov-Hausdorff distance. We show that the Euclidean plane and Gromov hyperbolic geodesic spaces with bounded geometry are approximable by uniform graphs, and pose a number of open problems.
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Additional Information
  • Dmitri Burago
  • Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
  • Email: burago@math.psu.edu
  • Sergei Ivanov
  • Affiliation: St. Petersburg Department of Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
  • ORCID: 0000-0002-4973-5935
  • Email: svivanov@pdmi.ras.ru
  • Received by editor(s): October 12, 2012
  • Received by editor(s) in revised form: June 25, 2013
  • Published electronically: October 16, 2014
  • Additional Notes: The first author was partially supported by NSF grant DMS-1205597.
    The second author was partially supported by RFBR grant 11-01-00302-a.
  • Communicated by: Kevin Whyte
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 1241-1256
  • MSC (2010): Primary 51K05, 05C12
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12299-4
  • MathSciNet review: 3293739