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

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

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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

Information

Published: Summer 2007
First available in Project Euclid: 13 November 2009

zbMATH: 1126.49037
MathSciNet: MR2342665
Digital Object Identifier: 10.1215/ijm/1258138420

Subjects:
Primary: 49Q10
Secondary: 57M25 , 58E10

Rights: Copyright © 2007 University of Illinois at Urbana-Champaign

Vol.51 • No. 2 • Summer 2007
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