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- Möbius_energy abstract "In mathematics, the Möbius energy of a knot is a particular knot energy, i.e. a functional on the space of knots. It was discovered by Jun O'Hara, who demonstrated that the energy blows up as the knot's strands get close to one another. This is a useful property because it prevents self-intersection and ensures the result under gradient descent is of the same knot type.Invariance of Möbius energy under Möbius transformations was demonstrated by Freedman, He, and Wang (1994) who used it to show the existence of a C1,1 energy minimizer in each isotopy class of a prime knot. They also showed the minimum energy of any knot conformation is achieved by a round circle.Conjecturally, there is no energy minimizer for composite knots. Kusner and Sullivan have done computer experiments with a discretized version of the Möbius energy and concluded that there should be no energy minimizer for the knot sum of two trefoils (although this is not a proof).".
- Möbius_energy wikiPageID "17716960".
- Möbius_energy wikiPageLength "2288".
- Möbius_energy wikiPageOutDegree "19".
- Möbius_energy wikiPageRevisionID "674828214".
- Möbius_energy wikiPageWikiLink Almgren–Pitts_min-max_theory.
- Möbius_energy wikiPageWikiLink André_Neves.
- Möbius_energy wikiPageWikiLink Annals_of_Mathematics.
- Möbius_energy wikiPageWikiLink Category:Knot_theory.
- Möbius_energy wikiPageWikiLink Connected_sum.
- Möbius_energy wikiPageWikiLink Fernando_Codá_Marques.
- Möbius_energy wikiPageWikiLink Gradient_descent.
- Möbius_energy wikiPageWikiLink Hopf_link.
- Möbius_energy wikiPageWikiLink Ian_Agol.
- Möbius_energy wikiPageWikiLink Jun_OHara.
- Möbius_energy wikiPageWikiLink Knot_(mathematics).
- Möbius_energy wikiPageWikiLink Knot_energy.
- Möbius_energy wikiPageWikiLink Knot_sum.
- Möbius_energy wikiPageWikiLink Knot_type.
- Möbius_energy wikiPageWikiLink Link_(knot_theory).
- Möbius_energy wikiPageWikiLink Mathematics.
- Möbius_energy wikiPageWikiLink Michael_Freedman.
- Möbius_energy wikiPageWikiLink Michael_H._Freedman.
- Möbius_energy wikiPageWikiLink Möbius_transformation.
- Möbius_energy wikiPageWikiLink Prime_knot.
- Möbius_energy wikiPageWikiLink Stereographic_projection.
- Möbius_energy wikiPageWikiLinkText "Möbius energy".
- Möbius_energy wikiPageWikiLinkText "Möbius energy#Freedman–He–Wang conjecture".
- Möbius_energy hasPhotoCollection Möbius_energy.
- Möbius_energy wikiPageUsesTemplate Template:Citation.
- Möbius_energy wikiPageUsesTemplate Template:Knottheory-stub.
- Möbius_energy wikiPageUsesTemplate Template:Reflist.
- Möbius_energy subject Category:Knot_theory.
- Möbius_energy comment "In mathematics, the Möbius energy of a knot is a particular knot energy, i.e. a functional on the space of knots. It was discovered by Jun O'Hara, who demonstrated that the energy blows up as the knot's strands get close to one another.".
- Möbius_energy label "Möbius energy".
- Möbius_energy sameAs m.047ttdl.
- Möbius_energy sameAs Q17098990.
- Möbius_energy sameAs Q17098990.
- Möbius_energy wasDerivedFrom Möbius_energy?oldid=674828214.
- Möbius_energy isPrimaryTopicOf Möbius_energy.