Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds

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dc.creatorHardin, D. P.
dc.creatorSaff, E. B.
dc.date2003-11-14
dc.date2004-12-15
dc.date.accessioned2026-07-07T04:30:43Z
dc.date.available2026-07-07T04:30:43Z
dc.descriptionFor a compact set A in Euclidean space we consider the asymptotic behavior of optimal (and near optimal) N-point configurations that minimize the Riesz s-energy (corresponding to the potential 1/t^s) over all N-point subsets of A, where s>0. For a large class of manifolds A having finite, positive d-dimensional Hausdorff measure, we show that such minimizing configurations have asymptotic limit distribution (as N tends to infinity with s fixed) equal to d-dimensional Hausdorff measure whenever s>d or s=d. In the latter case we obtain an explicit formula for the dominant term in the minimum energy. Our results are new even for the case of the d-dimensional sphere.
dc.descriptionpaper: 29 pages and addendum: 4 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0311024
dc.identifierhttp://arxiv.org/abs/math-ph/0311024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57563
dc.subjectMathematical Physics
dc.subjectGeneral Mathematics
dc.subjectMetric Geometry
dc.subject11K41, 70F10, 28A78, 78A30, 52A40
dc.titleMinimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds
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