Communications in Analysis and Geometry

Volume 12 (2004)

Number 4

The Apollonian Inner Metric

Pages: 927 – 947

DOI: http://dx.doi.org/10.4310/CAG.2004.v12.n4.a7

Author

Peter A. Häströ

Abstract

In this paper we derive an explicit formula for the inner metric of the Apollonian metric and prove that for most domains there exists a geodesic connecting two arbitrary points. We also give a necessary and sufficient condition for the Apollonian inner metric to be bilipschitz equivalent to the quasihyperbolic metric.

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