On the maximal product of distances between points on a sphere
For a set \(\{x_1, \dots, x_n\}\) of \(n\) points on the unit sphere \(S^2= \{x\in \mathbb{R}^n \mid|x|=1\}\), let \(M_n\) be the maximum of the product of their mutual euclidean distances. The determination of \(M_n\) has various mathematical and nonmathematical applications, and \(\lim M_n^{2/n(n-1)}\) for \(n\to\infty\) is called the transfinite diameter of \(S^2\). The author gives an upper bound for \(M_n\) and a lower bound for the distance of two points of the extremal (and not necessarily unique) spherical distribution.
scientific article; zbMATH DE number 1059785