Perfect, strongly eutactic lattices are periodic extreme

Details Perfect, strongly eutactic lattices are periodic extreme Perfect, strongly eutactic lattices are periodic extreme

2008-08-14

arxiv.org/abs/0808.2013v2

Advances in Mathematics 225 (2010), 2546-2564

Mathematics

Metric Geometry

20 pages, 1 table; some corrections, incorporated referee suggestions

Scientific paper

10.1016/j.aim.2010.05.002

We introduce a parameter space for periodic point sets, given as unions of $m$ translates of point lattices. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a periodic sphere packing with greater density. This applies in particular to the densest known lattice sphere packings in dimension $d\leq 8$ and $d=24$.

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