# Polarization Optimality of Equally Spaced Points on the Circle for Discrete Potentials

Discrete & Computational Geometry, Apr 2013

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 \begin{aligned} \sum _{k=1}^n f(d(z,z_k)), \end{aligned} where $f:[0,\pi ]\rightarrow [0,\infty ]$ is non-increasing and convex and $d(z,w)$ denotes the geodesic distance between z and w on the circle.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs00454-013-9502-4.pdf

Douglas P. Hardin, Amos P. Kendall, Edward B. Saff. Polarization Optimality of Equally Spaced Points on the Circle for Discrete Potentials, Discrete & Computational Geometry, 2013, 236-243, DOI: 10.1007/s00454-013-9502-4