Metric space inversions, quasihyperbolic distance, and uniform spaces Stephen BuckleyDavid HerronXiangdong Xie 51F9930C6530F45inversionsphericalizationquasimobiusquasihyperbolic metricuniform space 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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3193 10.1512/iumj.2008.57.3193 en Indiana Univ. Math. J. 57 (2008) 837 - 890 state-of-the-art mathematics http://iumj.org/access/