Periodicity and Circle Packing in the Hyperbolic Plane
| dc.creator | Bowen, Lewis | |
| dc.date | 2003-04-22 | |
| dc.date | 2003-09-03 | |
| dc.date.accessioned | 2026-07-07T04:57:16Z | |
| dc.date.available | 2026-07-07T04:57:16Z | |
| dc.description | 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. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304344 | |
| dc.identifier | http://arxiv.org/abs/math/0304344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67205 | |
| dc.subject | Metric Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 52A40 | |
| dc.title | Periodicity and Circle Packing in the Hyperbolic Plane | |
| dc.type | text |