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

摘要

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 emph{Clifford links}, that is, the conformal images of the standard geometric Hopf link.