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Buckley, Stephen M., 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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Official URL: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2008/57/...
Abstract
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 |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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