Polarization optimality of equally spaced points on the circle for discrete potentials

Abstract

We prove a conjecture of Ambrus, Ball and Erdélyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form \sum_{k=1}^n f(d(z,z_k)), where $f:[0,\pi ]\to [0,\infty ]$ is non-increasing and strictly convex and $d(z,w)$ denotes the geodesic distance between $z$ and $w$ on the circle.

8 pages, 1 figure, to appear Discrete and Computational Geometry

References in corpus (1)

• Analytic and Probabilistic Problems in Discrete Geometry

Cited by in corpus (2)

• Riesz Polarization Inequalities in Higher Dimensions
• On extremums of sums of powered distances to a finite set of points