Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

Details Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

2008-05-31

arxiv.org/abs/0806.0097v1

Mathematics

Complex Variables

14 pages, 1 latex file, 1 eps figure

Scientific paper

We obtain 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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