Geodesic
Osculatory Packings by Spheres
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 59-64

Voir la notice de l'article provenant de la source Cambridge University Press

If U is an open set in Euclidean N-space EN which has finite Lebesgue measure |U| then a complete packing of U by open spheres is a collection C={Sn } of pairwise disjoint open spheres contained in U and such that Σ∞ n=1|Sn | = |U|. Such packings exist by Vitali's theorem. An osculatory packing is one in which the spheres S n are chosen recursively so that from a certain point on S n+1 is the largest possible sphere contained in (Here S - will denote the closure of a set S). We give here a simple proof of the "well-known" fact that an osculatory packing is a complete packing. Our method of proof shows also that for osculatory packings, the Hausdorff dimension of the residual set is dominated by the exponent of convergence of the radii of the Sn . 
Boyd, David W. Osculatory Packings by Spheres. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 59-64. doi: 10.4153/CMB-1970-012-2
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