Annales Academić Scientiarum Fennicć
Mathematica
Volumen 32, 2007, 279-288

GROMOV HYPERBOLICITY OF CERTAIN CONFORMAL INVARIANT METRICS

Henri Lindén

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; hlinden 'at' cc.helsinki.fi

Abstract. The unit ball Bⁿ is shown to be Gromov hyperbolic with respect to the Ferrand metric \lambda^*_Bn and the modulus metric \mu_Bn, and dimension dependent upper bounds for the Gromov delta are obtained. In the two-dimensional case Gromov hyperbolicity is proved for all simply connected domains G. For \lambda^*_G also the case G = Rⁿ \ {0} is studied.

2000 Mathematics Subject Classification: Primary 30F45; Secondary 30C20.

Key words: Conformal modulus, modulus metric, Ferrand's metric, Gromov hyperbolic.

Reference to this article: H. Lindén: Gromov hyperbolicity of certain conformal invariant metrics. Ann. Acad. Sci. Fenn. Math. 32 (2007), 279-288.

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