Energy minimization, periodic sets and spherical designs

Abstract

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.

16 pages; incorporated referee comments

References in corpus (1)

• Ground states and formal duality relations in the Gaussian core model

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