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Geometric characterizations of Gromov hyperbolicity

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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.

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Correspondence to Zoltán M. Balogh or Stephen M. Buckley.

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Mathematics Subject Classification (1991)

30F45

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Balogh, Z., Buckley, S. Geometric characterizations of Gromov hyperbolicity. Invent. math. 153, 261–301 (2003). https://doi.org/10.1007/s00222-003-0287-6

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  • DOI: https://doi.org/10.1007/s00222-003-0287-6

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