Min-max theory and the energy of links (Q2792319)
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scientific article; zbMATH DE number 6552405
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Min-max theory and the energy of links |
scientific article; zbMATH DE number 6552405 |
Statements
Min-max theory and the energy of links (English)
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9 March 2016
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conformal knot energy
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minimizer
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Hopf link
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min-max theory
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This paper is on Möbius energies of knots first introduced by O'Hara (energies invariant under Möbius transformations of the plane). The authors prove that the stereographic projection of the standard Hopf link minimizes the Möbius energy among the class of all nontrivial links in Euclidean space. This statement was a conjectured by \textit{M. H. Freedman, Z. X. He} and \textit{Z. Wang} in [Ann. Math. (2) 139, No.1, 1--50 (1994; Zbl 0817.57011)]. The conjecture is proved using the min-max theory of minimal surfaces.
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