JournalsjemsVol. 22, No. 6pp. 1917–1970

Quasihyperbolic geodesics are hyperbolic quasi-geodesics

  • Stephen M. Buckley

    National University of Ireland, Maynooth, Ireland

  • David A. Herron

    University of Cincinnati, USA
Quasihyperbolic geodesics are hyperbolic quasi-geodesics cover

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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 quantitatively the same curves. We also demonstrate the simultaneous Gromov hyperbolicity of such domains with their hyperbolic or quasihyperbolic distances.

Cite this article

Stephen M. Buckley, David A. Herron, Quasihyperbolic geodesics are hyperbolic quasi-geodesics. J. Eur. Math. Soc. 22 (2020), no. 6, pp. 1917–1970

DOI 10.4171/JEMS/959