Buckley, Stephen M. and Herron, David A. and Xie, Xiangdong
Metric space inversions, quasihyperbolic distance, and uniform spaces.
Indiana University Mathematics Journal, 57 (2).
We dene 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.
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