JournalsggdVol. 1, No. 3pp. 281–299

A characterization of hyperbolic spaces

  • Indira Chatterji

    Ohio State University, Columbus, United States
  • Graham A. Niblo

    University of Southampton, UK
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Abstract

We show that a geodesic metric space, and in particular the Cayley graph of a finitely generated group, is hyperbolic in the sense of Gromov if and only if intersections of any two metric balls is itself “almost” a metric ball. In particular, R-trees are characterized among the class of geodesic metric spaces by the property that the intersection of any two metric balls is always a metric ball. A variation on the definition of “almost” allows us to characterise CAT(κ) geometry for κ ≤ 0 in the same way.

Cite this article

Indira Chatterji, Graham A. Niblo, A characterization of hyperbolic spaces. Groups Geom. Dyn. 1 (2007), no. 3, pp. 281–299

DOI 10.4171/GGD/13