Geometriae Dedicata

, Volume 102, Issue 1, pp 213–236

Periodicity and Circle Packings of the Hyperbolic Plane

  • Lewis Bowen

DOI: 10.1023/B:GEOM.0000006580.47816.e9

Cite this article as:
Bowen, L. Geometriae Dedicata (2003) 102: 213. doi:10.1023/B:GEOM.0000006580.47816.e9


We prove that given a fixed radius r, the set of isometry-invariant probability measures supported on 'periodic' radius r-circle packings of the hyperbolic plane is dense in the space of all isometry-invariant probability measures on the space of radius r-circle packings. By a periodic packing, we mean one with cofinite symmetry group. As a corollary, we prove the maximum density achieved by isometry-invariant probability measures on a space of radius r-packings of the hyperbolic plane is the supremum of densities of periodic packings. We also show that the maximum density function varies continuously with radius.

circle packing densest packings hyperbolic plane invariant measures optimal density 

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Lewis Bowen
    • 1
  1. 1.Department of MathematicsDavisU.S.A.

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