Communications in Analysis and Geometry

Volume 12 (2004)

Number 4

The Apollonian Inner Metric

Pages: 927 – 947



Peter A. Häströ


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.

Published 1 January 2004