Title: Metric space inversions, quasihyperbolic distance, and uniform spaces

Authors: Stephen M. Buckley, David A. Herron and Xiangdong Xie

Issue: Volume 57 (2008), Issue 2, 837-890

Abstract: We define a notion of inversion valid in the general metric space setting. We establish several basic facts concerning inversions; e.g., they are quasimöbius homeomorphisms and quasihyperbolically bilipschitz. In a certain sense, inversion is dual to sphericalization. We demonstrate that both inversion and sphericalization preserve local quasiconvexity and annular quasiconvexity as well as uniformity.