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, R-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 CAT(κ) geometry for κ≤0 in the same way.
1
Ohio State University, Columbus, United States
2
University of Southampton, UK
Indira Chatterji; Graham A. Niblo. A characterization of hyperbolic spaces. Groups, geometry, and dynamics, Tome 1 (2007) no. 3, pp. 281-299. doi: 10.4171/ggd/13
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title = {A characterization of hyperbolic spaces},
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year = {2007},
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