Energy minimization, periodic sets and spherical designs

Details Energy minimization, periodic sets and spherical designs Energy minimization, periodic sets and spherical designs

2010-05-24

arxiv.org/abs/1005.4373v2

Mathematics

Metric Geometry

16 pages; incorporated referee comments

Scientific paper

10.1093/imrn/rnr048

We study energy minimization for pair potentials among periodic sets in Euclidean spaces. We derive some sufficient conditions under which a point lattice locally minimizes the energy associated to a large class of potential functions. This allows in particular to prove a local version of Cohn and Kumar's conjecture that $\mathsf{A}_2$, $\mathsf{D}_4$, $\mathsf{E}_8$ and the Leech lattice are globally universally optimal, regarding energy minimization, and among periodic sets of fixed point density.

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