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Links of tori and the energy of incompressible flows. (English) Zbl 0731.57003

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.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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