Sphericalizations and applications in Gromov hyperbolic spaces

Abstract

In this paper, we study certain applications of sphericalization in Gromov hyperbolic metric spaces. We first show that doubling properties regarding two classes of metrics on the Gromov boundaries of hyperbolic spaces are equivalent. Second, we obtain a characterization of unbounded Gromov hyperbolic domains via the metric space sphericalization. Finally, we show that there is a homeomorphic correspondence between the Gromov boundary and the inner metric boundary of a Gromov hyperbolic domain which is φ-uniform.