Hästö, PeterLindén, HenriPortilla, AnaRodríguez, José M.Tourís, Eva2010-01-182010-01-182008-05arXiv:0806.0097v1https://hdl.handle.net/10016/647215 pages, 2 figures.-- MSC2000 codes: 30F45, 53C23, 30C99.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.0097SubmittedWe derive 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.application/pdfengPoincaré metricHyperbolic metricQuasihyperbolic metricGromov hyperbolicityDenjoy domainresearch articleMatemáticasopen access