Uniform approximation of metrics by graphs

Dmitri Burago, Sergei Ivanov

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1241-1256
Number of pages16
JournalProceedings of the American Mathematical Society
Volume143
Issue number3
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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