The boundary correspondence of some hyperbolic space

Abstract

Suppose that (X,d) is a complete metric space and M is a nonempty closed proper subset of X. Let μM be the Gromov hyperbolic metric on X∖M defined by Z. Ibragimov. In this paper, we show that there exists a natural quasisymmetric correspondence between the Gromov boundary of (X∖M,μM) and its metric boundary ∂M.