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January, 2012 Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics
Peter HÄSTÖ, Henri LINDÉN, Ana PORTILLA, José M. RODRÍGUEZ, Eva TOURÍS
J. Math. Soc. Japan 64(1): 247-261 (January, 2012). DOI: 10.2969/jmsj/06410247

Abstract

We derive explicit and simple conditions which in many cases allow one to decide, whether or not a Denjoy domain endowed with the Poincaré or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows us to deduce the non-hyperbolicity of any periodic Denjoy domain.

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Peter HÄSTÖ. Henri LINDÉN. Ana PORTILLA. José M. RODRÍGUEZ. Eva TOURÍS. "Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics." J. Math. Soc. Japan 64 (1) 247 - 261, January, 2012. https://doi.org/10.2969/jmsj/06410247

Information

Published: January, 2012
First available in Project Euclid: 26 January 2012

zbMATH: 1262.30044
MathSciNet: MR2879744
Digital Object Identifier: 10.2969/jmsj/06410247

Subjects:
Primary: 30F45
Secondary: 30C99 , 53C23

Keywords: Denjoy domain , Gromov hyperbolic , hyperbolic metric , Poincaré metric , quasihyperbolic metric

Rights: Copyright © 2012 Mathematical Society of Japan

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Vol.64 • No. 1 • January, 2012
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