Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-27T01:52:01.815Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)