2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162058We 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 figureComplex VariablesMetric Geometry30F45; 53C23, 30C99text