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Möbius-invariant metrics

Published online by Cambridge University Press:  01 January 1999

PASI SEITTENRANTA
PASI SEITTENRANTA
Affiliation:
University of Helsinki, Department of Mathematics, Nokia Research Center, P.O. Box 407, FIN-00045 Nokia Group, Finland; e-mail: pasi.seittenranta@research.nokia.com
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Abstract

A new Möbius-invariant metric δG defined on an open set G⊂[Rmacron]n with at least two boundary points is introduced. This metric coincides with the hyperbolic metric if G is the unit ball. Some inequalities between this and other metrics are proved.

The behaviour of δG under K-quasiconformal maps is also studied. In particular, a generalization of the Schwarz lemma is obtained for K-quasiconformal maps defined on quasiballs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 3 , January 1999 , pp. 511 - 533
Copyright
Cambridge Philosophical Society 1999

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