A real variable characterization of Gromov hyperbolicity of flute surfaces

Details A real variable characterization of Gromov hyperbolicity of flute surfaces A real variable characterization of Gromov hyperbolicity of flute surfaces

2008-05-31

arxiv.org/abs/0806.0093v1

Mathematics

Complex Variables

23 pages, 1 latex file, 2 eps figures

Scientific paper

In this paper we give a characterization of the Gromov hyperbolicity of trains (a large class of Denjoy domains which contains the flute surfaces) in terms of the behavior of a real function. This function describes somehow the distances between some remarkable geodesics in the train. This theorem has several consequences; in particular, it allows to deduce a result about stability of hyperbolicity, even though the original surface and the modified one are not quasi-isometric.

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