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 **B**^{n}
is shown to be Gromov hyperbolic with respect to the
Ferrand metric \lambda^{*}_{B}*n*
and the modulus metric \mu_{B}*n*,
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* = **R**^{n} \ {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.

Full document as PDF file

Copyright © 2007 by Academia Scientiarum Fennica