Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2012Embargo end date: 01 Jan 2008Publisher:Mathematical Society of Japan (Project Euclid)Journal:Journal of the Mathematical Society of Japan, volume 64 (issn: 0025-5645,

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Authors: HÄSTÖ, Peter; LINDÉN, Henri; PORTILLA, Ana; RODRÍGUEZ, José M.; TOURÍS, Eva;

doi: 10.2969/jmsj/06410247 , 10.48550/arxiv.0806.0097

arXiv: 0806.0097

handle: 10016/6472

Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

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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.

14 pages, 1 latex file, 1 eps figure

Related Organizations

Saint Louis University
United States
Carlos III University Madrid (UC3M)
Spain
University of Helsinki
Finland
Carlos III University of Madrid
Spain

Keywords

Hyperbolic metric, quasihyperbolic metric, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, Matemáticas, Mathematics - Complex Variables, Geometric function theory, Metric Geometry (math.MG), 53C23, 30C99, hyperbolic metric, Denjoy domain, Poincaré metric, 30F45, Gromov hyperbolicity, Mathematics - Metric Geometry, 30F45; 53C23, 30C99, Gromov hyperbolic, FOS: Mathematics, 53C23, 30C99, Complex Variables (math.CV), Quasihyperbolic metric, Conformal metrics (hyperbolic, Poincaré, distance functions)

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