Geometriae Dedicata

, Volume 163, Issue 1, pp 193–213 | Cite as

An upper bound on density for packings of collars about hyperplanes in \({\mathbb{H}^n}\)

Original Paper

Abstract

We consider packings of radius r collars about hyperplanes in \({\mathbb{H}^n}\). For such packings, we prove that the Delaunay cells are truncated ultra-ideal simplices which tile \({\mathbb{H}^n}\). If we place n + 1 hyperplanes in \({\mathbb{H}^n}\) each at a distance of exactly 2r to the others, we could place radius r collars about these hyperplanes. The density of these collars within the corresponding Delaunay cell is an upper bound on density for all packings of radius r collars.

Keywords

Density Hyperplanes Delaunay Hyperbolic geometry 

Mathematics Subject Classification (2000)

51M09 52C17 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsCollege of CharlestonCharlestonUSA

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