Geometric characterizations of Gromov hyperbolicity

We prove the equivalence of three different geometric properties of metric-measure spaces with controlled geometry. The first property is the Gromov hyperbolicity of the quasihyperbolic metric. The second is a slice condition and the third is a combination of the Gehring-Hayman property and a separa...

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Bibliographic Details
Published in:Inventiones mathematicae 2003-08, Vol.153 (2), p.261-301
Main Authors: Balogh, Zolt n M., Buckley, Stephen M.
Format: Article
Language:English
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Summary:We prove the equivalence of three different geometric properties of metric-measure spaces with controlled geometry. The first property is the Gromov hyperbolicity of the quasihyperbolic metric. The second is a slice condition and the third is a combination of the Gehring-Hayman property and a separation condition. [PUBLICATION ABSTRACT]
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-003-0287-6