A lower bound for the logarithmic energy on ${\mathbb{S}}^2$ and for the Green energy on ${\mathbb{S}}^n$

Abstract

We show an alternative proof of the sharpest known lower bound for the logarithmic energy on the unit sphere ${\mathbb{S}}^2$. We then generalize this proof to get new lower bounds for the Green energy on the unit $n$-sphere ${\mathbb{S}}^n$.

17 pages