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dc.contributor.authorBondarenko, A. V.
dc.contributor.authorHardin, Douglas P.
dc.contributor.authorSaff, Edward B.
dc.date.accessioned2016-09-22T10:46:38Z
dc.date.available2016-09-22T10:46:38Z
dc.date.issued2013-06-10
dc.identifier.urihttp://publications.mfo.de/handle/mfo/197
dc.descriptionOWLF 2013en_US
dc.description.abstractFor $N$-point best-packing configurations $\omega_N$ on a compact metric space $(A, \rho)$, we obtain estimates for the mesh-separation ratio $\gamma(\rho_N , A)$, which is the quotient of the covering radius of $\omega_N$ relative to $A$ and the minimum pairwise distance between points in $\omega_N$ . For best-packing configurations $\omega_N$ that arise as limits of minimal Riesz $s$-energy configurations as $s \to \infty$, we prove that $\gamma(\omega_N , A) ≤ 1$ and this bound can be attained even for the sphere. In the particular case when $N = 5$ on $S^1$ with $\rho$ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $\omega^*_5$, that is the limit (as $s \to \infty$) of 5-point $s$-energy minimizing configurations. Moreover, $\gamma(\omega^*_5, S^2) = 1$.
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2013,13
dc.subjectBest-Packingen_US
dc.subjectMesh Normen_US
dc.subjectSeparation Distanceen_US
dc.subjectQuasi-Uniformityen_US
dc.subjectRiesz Energyen_US
dc.subjectCovering Constanten_US
dc.titleMesh Ratios for Best-Packing and Limits of Minimal Energy Configurationsen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2013-13
local.scientificprogramOWLF 2013
local.series.idOWP-2013-13
local.subject.msc31
local.subject.msc65
local.subject.msc57
local.subject.msc52
local.subject.msc28


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