On densest packings of equal balls of $\rb^{n}$ and Marcinkiewicz spaces

Details On densest packings of equal balls of $\rb^{n}$ and Marcinkiewicz spaces On densest packings of equal balls of $\rb^{n}$ and Marcinkiewicz spaces

2008-12-09

arxiv.org/abs/0812.1720v1

Mathematics

Metric Geometry

20 pages. CIRM: Rencontre "Interface entre Analyse Harmonique et Th\'eorie des Nombres", Octobre 2005, to appear

Scientific paper

We investigate, by "a la Marcinkiewicz" techniques applied to the (asymptotic) density function, how dense systems of equal spheres of $\rb^{n}, n \geq 1,$ can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the systems of balls in the sense of Marcinkiewicz. Existence Theorems for densest sphere packings and completely saturated sphere packings of maximal density are given new direct proofs.

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