Application of an idea of VoronoA to lattice packing

作者：Gruber Peter M^*

来源：Annali di Matematica Pura ed Applicata, 2014, 193(4): 939-959.

DOI：10.1007/s10231-012-0308-4

• Voronoi type result
• Lattice packing of balls
• Lattice packing of convex bodies
• Maximum density
• Maximum lattice
• Perfect lattice
• Eutactic lattice

The geometric variant of a criterion of VoronoA says, a lattice packing of balls in has (locally) maximum density if and only if it is eutactic and perfect. This article deals with refinements of VoronoA%26apos;s result and extensions to lattice packings of smooth convex bodies. Versions of eutaxy and perfection are used to characterize lattices with semi-stationary, stationary, maximum and ultra-maximum lattice packing density, where ultra-maximality is a sharper version of maximality. Surprisingly, for balls, the lattice packings with maximum density have ultra-maximum density. To make the picture more complete, for , we specify the lattices that provide lattice packings of balls with maximum properties. These lattices are related to Bravais types. Finally, similar results of a duality type are given.

• 出版日期2014-8