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A characterization of hyperbolic spaces

Indira Chatterji·Graham A. Niblo
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Abstract

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($κ$) geometry can be characterised in terms of the geometry of the intersection of balls.

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Indira Chatterji, Graham A. Niblo. 2006-05-19. A characterization of hyperbolic spaces. https://arxiv.org/abs/math/0410035

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