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March 2011 A real variable characterization of Gromov hyperbolicity of flute surfaces
Ana Portilla, José M. Rodríguez, Eva Tourís
Osaka J. Math. 48(1): 179-207 (March 2011).


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. In order to obtain these results we also prove some trigonometric lemmas that are interesting by themselves, since they provide very simple estimates on some hyperbolic distances.


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Ana Portilla. José M. Rodríguez. Eva Tourís. "A real variable characterization of Gromov hyperbolicity of flute surfaces." Osaka J. Math. 48 (1) 179 - 207, March 2011.


Published: March 2011
First available in Project Euclid: 22 March 2011

zbMATH: 1259.53044
MathSciNet: MR2802598

Primary: 41A10, 46E35, 46G10

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics


Vol.48 • No. 1 • March 2011
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