Min-max theory and the energy of links
Ian Agol, Fernando C. Marques, Andr\'e Neves
TL;DR
This paper proves a longstanding conjecture that the Mobius energy of links is minimized by the stereographic projection of the Hopf link, using min-max theory of minimal surfaces.
Contribution
It introduces a novel application of min-max theory to link energies, confirming the conjecture about Mobius energy minimization.
Findings
Mobius energy minimized by stereographic Hopf link
Confirmation of Freedman, He, and Wang's conjecture
Application of min-max theory to link energies
Abstract
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.
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