A characterization of hyperbolic spaces

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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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Group Theory, 20F67; 20F65; 20E08

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http://salesiana.dossiersoluciones.com/handle/123456789/132115

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410035
 http://arxiv.org/abs/math/0410035
 Groups, Geometry and Dynamics, Volume 1, Issue 3 (2007) pp 281-299

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arXiv