descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Mar 2020Embargo end date: 01 Jan 2017Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Journal of the European Mathematical Society, volume 22, pages 1,917-1,970 (issn: 1435-9855, eissn: 1435-9863,

Authors: Herron, David A.; Buckley, Stephen M.;

doi: 10.4171/jems/959 , 10.48550/arxiv.1704.07193

arXiv: http://arxiv.org/abs/1704.07193

Quasihyperbolic geodesics are hyperbolic quasi-geodesics

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Abstract

This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hyperbolic and quasihyperbolic quasi-geodesics are quantitatively the same curves. We also demonstrate the simultaneous Gromov hyperbolicity of such domains with their hyperbolic or quasihyperbolic distances.

Related Organizations

Maynooth University
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Keywords

Mathematics - Metric Geometry, FOS: Mathematics, Primary: 30F45, 30L99, Secondary: 51F99, 53C22, 30C62, Metric Geometry (math.MG), 510

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