Geometric characterizations of Gromov hyperbolicity

• DOI: 10.1007/s00222-003-0287-6
• Publication Date: 2004-10-14T21:25:16Z
• Authors: Zolt�n M. Balogh; Stephen M. Buckley
• Keywords: 510 Mathematics; 0102 computer and information sciences; Mathematics & Statistics; 01 natural sciences; 510

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.