# Universal optimal configurations for the $p$-frame potentials

@article{Chen2020UniversalOC,
title={Universal optimal configurations for the \$p\$-frame potentials},
author={Xuemei Chen and Victor Gonzales and E. Goodman and Shujie Kang and K. Okoudjou},
year={2020},
volume={46},
pages={4}
}
Given $d, N\geq 2$ and $p\in (0, \infty]$ we consider a family of functionals, the $p$-frame potentials FP$_{p, N, d}$, defined on the set of all collections of $N$ unit-norm vectors in $\mathbb R^d$. For the special case $p=2$ and $p=\infty$, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals FP$_{p, N, d}$, by first establishing some general properties of their minima. Thereafter, we focus… Expand
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