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.
Categories: math.MG math-ph math.MP math.NT