Geometriae Dedicata

, Volume 121, Issue 1, pp 221–245

Gromov hyperbolicity of Denjoy Domains

  • Venancio Alvarez
  • Ana Portilla
  • Jose M. Rodriguez
  • Eva Touris
Original Paper

Abstract

In this paper we characterize the Gromov hyperbolicity of the double of a metric space. This result allows to give a characterization of the hyperbolic Denjoy domains, in terms of the distance to \(\mathbb{R}\) of the points in some geodesics. In the particular case of trains (a kind of Riemann surfaces which includes the flute surfaces), we obtain more explicit criteria which depend just on the lengths of what we have called fundamental geodesics.

Keywords

Denjoy domain Flute surface Gromov hyperbolicity Riemann surface Schottky double Train 

Mathematical Subject Classifications (2000)

41A10 46E35 46G10 

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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Venancio Alvarez
    • 2
  • Ana Portilla
    • 1
  • Jose M. Rodriguez
    • 1
  • Eva Touris
    • 1
  1. 1.Departamento de Matemáticas, Escuela Politécnica SuperiorUniversidad Carlos III de MadridMadridSpain
  2. 2.Departamento de Análisis MatemáticoFacultad de CienciasMálagaSpain

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