We derive explicit and simple conditions which in many cases allow one to decide, whether or not a Denjoy domain endowed with the Poincaré or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows us to deduce the non-hyperbolicity of any periodic Denjoy domain.
"Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics." J. Math. Soc. Japan 64 (1) 247 - 261, January, 2012. https://doi.org/10.2969/jmsj/06410247