Geodesic
Asymptotics for Minimal Discrete Riesz Energy on Curves in Rd
Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 529-552

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the $s$ -energy $E({{Z}_{n}};\,s)={{\Sigma }_{i\ne j}}K(\parallel {{z}_{i,n}}\,-\,{{z}_{j,n}}\parallel \,;\,s)$ for point sets $Zn\,=\,\{{{z}_{k,n}}\,:\,k\,=\,0,\,\ldots \,,\,n\} $ on certain compact sets $\Gamma $ in ${{\mathbb{R}}^{d}}$ having finite one-dimensional Hausdorff measure,where $$K(t;\,s)\,=\,\left\{ _{-\ln \,t,\,\,\,\text{if}\,s\,=\,0,\,}^{{{t}^{-s}},\,\,\,\,\,\,\,\text{if}\,s\,>\,0,} \right\}$$ is the Riesz kernel. Asymptotics for the minimum $s$ -energy and the distribution of minimizing sequences of points is studied. In particular, we prove that, for $s\,\ge \,1$ , the minimizing nodes for a rectifiable Jordan curve Γ distribute asymptotically uniformly with respect to arclength as $n\,\to \,\infty $ .
DOI : 10.4153/CJM-2004-024-1
Mots-clés : 52A40, 31C20, Riesz energy, Minimal discrete energy, Rectifiable curves, Best-packing on curves 
Martínez-Finkelshtein, A.; Maymeskul, V.; Rakhmanov, E. A.; Saff, E. B. Asymptotics for Minimal Discrete Riesz Energy on Curves in Rd. Canadian journal of mathematics, Tome 56 (2004) no. 3, pp. 529-552. doi: 10.4153/CJM-2004-024-1
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     title = {Asymptotics for {Minimal} {Discrete} {Riesz} {Energy} on {Curves} in {Rd}},
     journal = {Canadian journal of mathematics},
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     year = {2004},
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