Clifford links are the only minimizers of the zone modulus among non-split links

Abstract

The zone modulus is a conformally invariant functional over the space of two-component links embedded in $\mathbf{R}^3$ or $\mathbf{S}^3$. It is a positive real number and its lower bound is $1.$ Its main property is that the zone modulus of a non-split link is greater than $(1 + \sqrt{2})^2.$ In this paper, we will show that the only non-split links with modulus equal to $(1 + \sqrt{2})^2$ are the Clifford links, that is, the conformal images of the standard geometric Hopf link.