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1. CJM 2011 (vol 64 pp. 24)

Borodachov, S. V.
Lower Order Terms of the Discrete Minimal Riesz Energy on Smooth Closed Curves
We consider the problem of minimizing the energy of $N$ points repelling each other on curves in $\mathbb{R}^d$ with the potential $|x-y|^{-s}$, $s\geq 1$, where $|\, \cdot\, |$ is the Euclidean norm. For a sufficiently smooth, simple, closed, regular curve, we find the next order term in the asymptotics of the minimal $s$-energy. On our way, we also prove that at least for $s\geq 2$, the minimal pairwise distance in optimal configurations asymptotically equals $L/N$, $N\to\infty$, where $L$ is the length of the curve.

Keywords:minimal discrete Riesz energy, lower order term, power law potential, separation radius
Categories:31C20, 65D17

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