Periodicity and Circle Packings of the Hyperbolic Plane
- Cite this article as:
- Bowen, L. Geometriae Dedicata (2003) 102: 213. doi:10.1023/B:GEOM.0000006580.47816.e9
- 63 Downloads
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.