Discrete logarithmic energy on the sphere

P.D. Dragnev, D.A. Legg and D.W. Townsend

Vol. 207 (2002), No. 2, 345–358

DOI: 10.2140/pjm.2002.207.345

Abstract

In this article we consider the problem posed by Whyte, about the distribution of N point charges on the unit sphere, whose mutual distances have maximal geometric mean. Some properties of the extremal points are discussed. In the case when N = 5 the optimal configuration is established rigorously, which solves an open problem communicated by Rakhmanov.

Milestones

Published: 1 December 2002