A Very Simple Characterization of Gromov Hyperbolicity for a Special Kind of Denjoy Domains

Abstract

Abstract. In this paper we provide characterizations for the Gromov hyperbolicity of some particular Denjoy domains and besides some sufficient conditions to guarantee or discard the hyperbolicity of some others. The conditions obtained involve just the lengths of some special simple closed geodesics in the domain. These results, on the one hand, show the extraordinary complexity of determining the hyperbolicity of a domain and, on the other hand, allow us to construct easily a large variety of both hyperbolic and non-hyperbolic domains.