Computational Methods and Function Theory 4 (2004), No. 2, 249--273
Copyright Heldermann Verlag 2004
Peter A. Hästö
hasto@cc.helsinki.fi , Department of Mathematics and Statistics, P.O.Box 68, FIN-00014 University of Helsinki, Finland.
In this paper we consider domains in which the Apollonian metric is quasi-isotropic. We calculate optimal quasi-isotropy constants for exterior ball domains and several simple domains and show that in many cases the Apollonian metric can be globally approximated with Seittenranta's metric using the optimal quasi-isotropy constant.
Keywords: Apollonian metric, Barbilian metric, quasi-isotropy, exterior ball domains.
MSC 2000: Primary 30F45; Secondary 30C65.
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