dc.contributor.author Bondarenko, A. V. dc.contributor.author Hardin, Douglas P. dc.contributor.author Saff, Edward B. dc.date.accessioned 2016-09-22T10:46:38Z dc.date.available 2016-09-22T10:46:38Z dc.date.issued 2013-06-10 dc.identifier.uri http://publications.mfo.de/handle/mfo/197 dc.description OWLF 2013 en_US dc.description.abstract For $N$-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.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2013,13 dc.subject Best-Packing en_US dc.subject Mesh Norm en_US dc.subject Separation Distance en_US dc.subject Quasi-Uniformity en_US dc.subject Riesz Energy en_US dc.subject Covering Constant en_US dc.title Mesh Ratios for Best-Packing and Limits of Minimal Energy Configurations en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2013-13 local.scientificprogram OWLF 2013 local.series.id OWP-2013-13 local.subject.msc 31 local.subject.msc 65 local.subject.msc 57 local.subject.msc 52 local.subject.msc 28 dc.identifier.urn urn:nbn:de:101:1-2013061117486 dc.identifier.ppn 1652445161
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