Min-max theory and the energy of links
  Freedman, He, and Wang, conjectured in 1994 that the Mobius energy should be minimized, among the class of all nontrivial links in Euclidean space, by the stereographic projection of the standard Hopf link. We prove this conjecture using the min-max theory of minimal surfaces. 
Ian Agol, Fernando C. Marques, Andr\'e Neves
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