Gromov hyperbolicity of Denjoy Domains |
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| Authors: | Venancio Alvarez Ana Portilla Jose M Rodriguez Eva Touris |
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| Institution: | (1) Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911, Leganés, Madrid, Spain;(2) Departamento de Análisis Matemático, Facultad de Ciencias, Campus de Teatinos, 29071 Málaga, Spain |
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| 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  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.
Research partially supported by three grants from M.E.C. (MTM 2006-11976, MTM 2006-13000-C03-02 and MTM 2004-21420-E), Spain. |
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| Keywords: | Denjoy domain Flute surface Gromov hyperbolicity Riemann surface Schottky double Train |
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