A characterization of hyperbolic spaces
Indira Chatterji
Ohio State University, Columbus, United StatesGraham A. Niblo
University of Southampton, UK
![A characterization of hyperbolic spaces cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-1-issue-3.png&w=3840&q=90)
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, -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 geometry for 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