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  1. ; (, Annales Fennici mathematici)
    null (Ed.)
    In this note we show that given two complete geodesic Gromov hyperbolic spaces that are roughly isometric and an arbitrary (not necessarily small), either the uniformization of both spaces with parameter epsilon results in uniform domains, or else neither uniformized space is a uniform domain. The terminology of "uniformization" is from [BHK], where it is shown that the uniformization, with parameter epsilon, of a complete geodesic Gromov hyperbolic space results in a uniform domain provided epsilon is small enough. 
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