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    Quasi-Hyperbolic Geodesics are Hyperbolic Quasi-Geodesics


    Herron, David A. and Buckley, Stephen M. (2017) Quasi-Hyperbolic Geodesics are Hyperbolic Quasi-Geodesics. Journal of the European Mathematical Society (959). ISSN 1435-9855

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    Abstract

    This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hyperbolic and quasihyperbolic quasi-geodesics are the same curves. We also demonstrate the simultaneous Gromov hyperbolicity of such domains with their hyperbolic or quasihyperbolic distances.

    Item Type: Article
    Additional Information: This is the pre-publication version of the article, which will appear in Buckley Stephen, Herron David: Quasihyperbolic geodesics are hyperbolic quasi-geodesics. J. Eur. Math. Soc. Electronically published on March 5, 2020. doi: 10.4171/JEMS/959 (to appear in print)
    Keywords: Hyperbolic metric; quasihyperbolic metric; quasi-geodesics; Gromov hyperbolicity;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 13072
    Identification Number: https://doi.org/10.4171/JEMS/959
    Depositing User: Prof. Stephen Buckley
    Date Deposited: 19 Jun 2020 15:00
    Journal or Publication Title: Journal of the European Mathematical Society
    Publisher: Springer Verlag
    Refereed: Yes
    URI:

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