- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:57
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
1
2007
3
A characterization of hyperbolic spaces
Indira
Chatterji
Ohio State University, COLUMBUS, UNITED STATES
Graham
Niblo
University of Southampton, SOUTHAMPTON, UNITED KINGDOM
Gromov hyperbolic spaces, CAT(0) geometry, geodesic metric spaces
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.
Group theory and generalizations
General
281
299
10.4171/GGD/13
http://www.ems-ph.org/doi/10.4171/GGD/13