Optimal logarithmic energy points on the unit sphere

@article{Brauchart2008OptimalLE,
title={Optimal logarithmic energy points on the unit sphere},
author={Johann S. Brauchart},
journal={Math. Comput.},
year={2008},
volume={77},
pages={1599-1613}
}

We study minimum energy point charges on the unit sphere Sd in Rd+1, d ≥ 3, that interact according to the logarithmic potential log(1/r), where r is the Euclidean distance between points. Such optimal N-point configurations are uniformly distributed as N → ∞. We quantify this result by estimating the spherical cap discrepancy of optimal energy configurations. The estimate is of order O(N−1/(d+2)). Essential is an improvement of the lower bound of the optimal logarithmic energy which yields the… CONTINUE READING