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arXiv · 1005.4373

Energy minimization, periodic sets and spherical designs

Renaud Coulangeon·Achill Schürmann
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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.

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Renaud Coulangeon, Achill Schürmann. 2011-02-02. Energy minimization, periodic sets and spherical designs. https://doi.org/10.1093/imrn%2Frnr048

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