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    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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    Official URL: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2008/57/...


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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:

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