Energy minimization, periodic sets and spherical designs
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COULANGEON, Renaud | |
| hal.structure.identifier | Institut für Mathematik | |
| dc.contributor.author | SCHÜRMANN, Achill | |
| dc.date.accessioned | 2024-04-04T02:23:09Z | |
| dc.date.available | 2024-04-04T02:23:09Z | |
| dc.date.created | 2011-02-02 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189709 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.title.en | Energy minimization, periodic sets and spherical designs | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/imrn/rnr048 | |
| dc.subject.hal | Mathématiques [math]/Géométrie métrique [math.MG] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 1005.4373 | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.page | 829-848 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00775916 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00775916v1 | |
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