COULANGEON, Renaud; SCHÜRMANN, Achill

doi:10.1093/imrn/rnr048

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COULANGEON, Renaud
Institut de Mathématiques de Bordeaux [IMB]

SCHÜRMANN, Achill
Institut für Mathematik

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International Mathematics Research Notices. 2012 n° 4, p. 829-848

Oxford University Press (OUP)

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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.< Leer menos

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Energy minimization, periodic sets and spherical designs

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