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 R~3 or 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 + 2~(1/2))~2. In this paper, we will show that the only non-split links with modulus equal to (1 + 2~(1/2))~2 are the Clifford links, that is, the conformal images of the standard geometric Hopf link.