Metric space inversions, quasihyperbolic distance, and uniform spaces

Buckley, Stephen M. and Herron, David A. and Xie, Xiangdong (2008) Metric space inversions, quasihyperbolic distance, and uniform spaces. Indiana University Mathematics Journal, 57 (2). pp. 837-890. ISSN 0022-2518

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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.

Item Type: Article
Keywords: Inversion; Sphericalization; Quasimöbius; Quasihyperbolic metric; Uniform space.
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1610
Identification Number: 10.1512/iumj.2008.57.3193
Depositing User: Prof. Stephen Buckley
Date Deposited: 21 Oct 2009 09:38
Journal or Publication Title: Indiana University Mathematics Journal
Publisher: Department of Mathematics Indiana University
Refereed: No

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