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- W2069388909 abstract "THE MODULI of curve families have been a useful bridge between analysis and geometric-topological argument. Caratheodory exploited the notion to construct his theory of prime ends. In dimensions three and higher this connection has been extensively developed by Fred Gehring (For example, see [4] and [SJ). We continue in this tradition by showing that the naturally defined “conformal moduli” for a disjoint collection of solid tori in RJ cannot all be greater than the constant (125/‘4H)n if the tori are linked in any essential manner. It is natural to conjecture that the optimal lower bound is (‘.5 I)& the modulus of the “solid” Clifford 1orus.J As an application, WC use the topology of linking flow lines to cstimatc a lower bound on the cncrgy ofccrtain incompressible flows. Roughly, one thinks that an invariant solid torus of spinning fluid may give up cncrgy by elongating like a soda straw, but that this should bc prcvcntcd if scvcral such tori arc linked. To make this prccisc, an incquality relating modulus and a variant of energy is dcrivcd. For some pcrspcctivc and rcfcrcnccs on this problem the rcadcr may consult [3] and [6]. WC express our thanks to Michael Starbird for intcrcsting conversations on this subject. Let ‘fc R’ bc a solid torus. We define the modulus" @default.
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- W2069388909 date "1991-01-01" @default.
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- W2069388909 title "Links of tori and the energy of incompressible flows" @default.
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- W2069388909 doi "https://doi.org/10.1016/0040-9383(91)90014-u" @default.
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