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The Apollonian Metric: Quasi-Isotropy and Seittenranta’s Metric

Abstract

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.

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Correspondence to Peter A. Hästö.

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The author was financially supported by the Finnish Academy of Science and Letters and the Academy of Finland through the Graduate School of Analysis and Logic.

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Hästö, P.A. The Apollonian Metric: Quasi-Isotropy and Seittenranta’s Metric. Comput. Methods Funct. Theory 4, 249–273 (2005). https://doi.org/10.1007/BF03321068

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  • DOI: https://doi.org/10.1007/BF03321068

Key Words

  • Barbilian metric
  • quasi-isotropy
  • exterior ball domains

2000 MSC

  • 30F45
  • 30C65