Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

2008/05/31 by Peter Hästö, Henri Lindén, Hästö, Peter +10 · 1 citation
Mathematics · #30C99 #30F45 #53C23 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #math.CV #math.MG #msc:30C99 #msc:30F45 #msc:53C23

paper · pdf · doi:10.48550/arxiv.0806.0097

14 pages, 1 latex file, 1 eps figure

arxiv created 2008/05/31 · openalex publication_date 2008/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We obtain explicit and simple conditions which in many cases allow one decide, whether or not a Denjoy domain endowed with the Poincare or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows to deduce the non-hyperbolicity of any periodic Denjoy domain.

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