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.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
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