Periodicity and Circle Packing in the Hyperbolic Plane

dc.creatorBowen, Lewis
dc.date2003-04-22
dc.date2003-09-03
dc.date.accessioned2026-07-07T04:57:16Z
dc.date.available2026-07-07T04:57:16Z
dc.descriptionWe 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.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0304344
dc.identifierhttp://arxiv.org/abs/math/0304344
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67205
dc.subjectMetric Geometry
dc.subjectGroup Theory
dc.subject52A40
dc.titlePeriodicity and Circle Packing in the Hyperbolic Plane
dc.typetext

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