Geometry & Topology 4 (2000) 277–292

DOI: 10.2140/gt.2000.4.277

arXiv: math.MG/9908003

Abstract

The notion of a completely saturated packing [Monats. Math. 125 (1998) 127-145] is a sharper version of maximum density, and the analogous notion of a completely reduced covering is a sharper version of minimum density. We define two related notions: uniformly recurrent and weakly recurrent dense packings, and diffusively dominant packings. Every compact domain in Euclidean space has a uniformly recurrent dense packing. If the domain self-nests, such a packing is limit-equivalent to a completely saturated one. Diffusive dominance is yet sharper than complete saturation and leads to a better understanding of n–saturation.

Keywords

density, saturation, packing, covering, dominance

Mathematical Subject Classification

Primary: 52C15, 52C17

Secondary: 52B99, 52C20, 52C22, 52C26

References

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Publication

Received: 4 August 1999
Revised: 28 September 2000
Accepted: 21 September 2000
Published: 8 October 2000
Proposed: Robion Kirby
Seconded: Michael Freedman, Walter Neumann

Authors