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

Gilbert Muraz (1) , Jean-Louis Verger-Gaugry (1)

1 IF - Institut Fourier

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.

Mots clés: Delone set; Marcinkiewicz norm; density; sphere packing

Domaines: Géométrie métrique [math.MG]; Théorie des nombres [math.NT]

Gilbert Muraz, Jean-Louis Verger-Gaugry. On densest packings of equal balls of ~$\rb^{n}$~ and Marcinkiewicz spaces. 2008. ⟨hal-00345611⟩