UNIFORMLY SEPARATED SETS AND GROMOV HYPERBOLICITY OF DOMAINS WITH THE QUASIHYPERBOLIC METRIC

Abstract. In this article we prove comparative results on the Gromov hyperbolicity of plane domains equipped with the quasihyperbolic metric. By a comparative result we mean one which assumes hyperbolicity in one domain and obtains it in a different domain somehow related to the original one. We derive a characterization (simple to check in practical cases) of the Gromov hyperbolicity of a plane domain Ω ∗ obtained by deleting from the original domain Ω any uniformly separated union of compact sets. We present as well a result about stability of hyperbolicity. 1