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.
Citation
Grégoire-Thomas Moniot. "Clifford links are the only minimizers of the zone modulus among non-split links." Illinois J. Math. 51 (2) 397 - 407, Summer 2007. https://doi.org/10.1215/ijm/1258138420
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