Freedman, Michael H.; He, Zheng-Xu Links of tori and the energy of incompressible flows. (English) Zbl 0731.57003 Topology 30, No. 2, 283-287 (1991). The moduli of curve families have been a useful bridge between analysis and geometric-topological argument. On this line the authors show that the naturally defined “conformal moduli” for a disjoint collection of solid tori in \({\mathbb{R}}^ 3\) cannot all be greater than the constant (125/48)\(\pi\) if the tori are linked in any essential manner. As an application the topology of linking flow lines is used in order to estimate a lower bound on the energy of certain incompressible flows. Roughly, one thinks that an invariant solid torus of spinning fluid may give up energy by elongating like a soda straw, but that this should be prevented if several such tori are linked. More precisely, an inequality relating modulus and a variant of energy is derived. Reviewer: M.Craioveanu (Timişoara) Cited in 1 ReviewCited in 6 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) Keywords:curve families; linking flow lines; energy; incompressible flows PDFBibTeX XMLCite \textit{M. H. Freedman} and \textit{Z.-X. He}, Topology 30, No. 2, 283--287 (1991; Zbl 0731.57003) Full Text: DOI