Uniform cantor sets as hyperbolic boundaries

Abstract

In this paper, we prove that the Gromov hyperbolic space (?,h) which was introduced by Z. Ibragimov and J. Simanyi in [3] is an asymptotically PT??1 space and extend the methods of [3] to the case of uniform Cantor sets, show that the uniform Cantor set is isometric to the Gromov hyperbolic boundary at infinity of some asymptotically PT-1 space.