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A real variable characterization of Gromov hyperbolicity of flute surfaces

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URI: http://hdl.handle.net/10016/6469
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real_touris_ojm_2009_ps.pdf (215.21 KB)
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2008-05
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Abstract
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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23 pages, 1 figure.-- MSC2000 codes: 41A10, 46E35, 46G10.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.0093
Previously presented as Communication at International Congress of Mathematicians 2006 (ICM2006, Madrid, Spain, Aug 22-30, 2006).
Preaccepted for publication at: Osaka Journal of Mathematics
Keywords
Denjoy domain, Flute surface, Gromov hyperbolicity, Riemann surface of infinite type, Train
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arXiv:0806.0093v1
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