Optimizers of three-point energies and nearly orthogonal sets

Authors

Dmitriy Bilyk
Damir Ferizović
Alexey Glazyrin, The University of Texas Rio Grande Valley
Ryan Matzke
Josiah Park
Oleksandr Vlasiuk

Document Type

Article

Publication Date

2023

Abstract

This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of distances between points to the context of three-point potentials. In particular, we study three-point analogues of the sphere packing problem and the optimization problem for p-frame energies based on three points. It turns out that both problems are inherently connected to the problem of nearly orthogonal sets by Erdős. As the outcome, we provide a new solution of the Erdős problem from the three-point packing perspective. We also show that the orthogonal basis uniquely minimizes the p-frame three-point energy when 0

Recommended Citation

Bilyk, Dmitriy, et al. "Optimizers of three-point energies and nearly orthogonal sets." arXiv preprint arXiv:2303.12283 (2023).