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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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:	https://doi.org/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
URI:	Publisher
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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