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Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

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URI: https://hdl.handle.net/10016/6472
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gromov_touris_pre_2008_ps.pdf (181.33 KB)
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2008-05
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Abstract
We derive explicit and simple conditions which in many cases allow one decide, whether or not a Denjoy domain endowed with the Poincare or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. As a corollary, the main theorem allows to deduce the non-hyperbolicity of any periodic Denjoy domain.
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15 pages, 2 figures.-- MSC2000 codes: 30F45, 53C23, 30C99.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.0097
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Poincaré metric, Hyperbolic metric, Quasihyperbolic metric, Gromov hyperbolicity, Denjoy domain
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arXiv:0806.0097v1
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