Min-max theory and the energy of links. (English) Zbl 1335.57009

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 M. H. Freedman, Z. X. He and 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.


57M25 Knots and links in the \(3\)-sphere (MSC2010)
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
49Q20 Variational problems in a geometric measure-theoretic setting


Zbl 0817.57011
Full Text: DOI arXiv


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