Asymptotics of Best-Packing on Rectifiable Sets
  We investigate the asymptotic behavior, as $N$ grows, of the largest minimal pairwise distance of $N$ points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurations. For this purpose, we compare best-packing configurations with minimal Riesz $s$-energy configurations and determine the $s$-th root asymptotic behavior (as $s\to \infty)$ of the minimal energy constants.   We show that the upper and the lower dimension of a set defined through the Riesz energy or best-packing coincides with the upper and lower Minkowski dimension, respectively.   For certain sets in ${\rm {\bf R}}^d$ of integer Hausdorff dimension, we show that the limiting behavior of the best-packing distance as well as the minimal $s$-energy for large $s$ is different for different subsequences of the cardinalities of the configurations. 
S.V. Borodachov, D.P. Hardin, E.B. Saff