Characterizations of metric trees and Gromov hyperbolic spaces

Details Characterizations of metric trees and Gromov hyperbolic spaces Characterizations of metric trees and Gromov hyperbolic spaces

2006-03-22

arxiv.org/abs/math/0603539v2

Mathematics

Metric Geometry

minor changes in the structure, proof of Rademacher theorem for Lipschitz maps into metric spaces added, outline of proof adde

Scientific paper

In a recent paper Chatterji and Niblo proved that a geodesic metric space is Gromov hyperbolic if and only if the intersection of any two closed balls has uniformly bounded eccentricity. In their paper, the authors raise the question whether a geodesic metric space with the property that the intersection of any two closed balls has eccentricity 0, is necessarily a real tree. The purpose of this note is to answer this question affirmatively. We also partially improve the main result of Chatterji and Niblo by showing that already sublinear eccentricity implies Gromov hyperbolicity.

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