Document Type

Article

Publication Date

Spring 3-31-2016

Publication Source

Contemporary Mathematics

Volume

661

Inclusive pages

41-55

Publisher

American Mathematical Society

Peer Reviewed

invited

Abstract

In this article we consider the distribution of N points on the unit

sphere $S^{d−1}$ in $R^d$ interacting via logarithmic potential. A characterization

theorem of the stationary configurations is derived when $N = d + 2$ and two

new log-optimal configurations minimizing the logarithmic energy are obtained

for six points on $S^3$ and seven points on $S^4$. A conjecture on the log-optimal

configurations of $d + 2$ points on $S^{d−1}$ is stated and three auxiliary results

supporting the conjecture are presented.

Keywords

Discrete minimal energy, logarithmic energy, elliptic Fekete points, sharp configurations.

Disciplines

Analysis | Discrete Mathematics and Combinatorics | Mathematics

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Link to Original Published Item

http://arxiv.org/pdf/1504.02544.pdf