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 | |