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Energy minimization, periodic sets and spherical designs
Language
en
Article de revue
This item was published in
International Mathematics Research Notices. 2012 n° 4, p. 829-848
Oxford University Press (OUP)
English 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 ...Read more >
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.Read less <
Origin
Hal imported