A characterization of hyperbolic spaces

Details A characterization of hyperbolic spaces A characterization of hyperbolic spaces

2004-10-02

arxiv.org/abs/math/0410035v3

Groups, Geometry and Dynamics, Volume 1, Issue 3 (2007) pp 281-299

Mathematics

Group Theory

Scientific paper

We show that a geodesic metric space is hyperbolic in the sense of Gromov if and only if intersections of balls have bounded eccentricity. In particular, $\R$-trees are characterized among geodesic metric spaces by the property that the intersection of any two balls is always a ball. Both Gromov hyperbolicity and CAT($\kappa$) geometry can be characterised in terms of the geometry of the intersection of balls.

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