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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Möbius energy ： ウィキペディア英語版 Möbius energy 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 ''C''1,1 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). ==Freedman–He–Wang conjecture== The Freedman–He–Wang conjecture (1994) stated that the Möbius energy of nontrivial links in $\backslash Bbb\; R^3$ is minimized by the stereographic projection of the standard Hopf link. This was proved in 2012 by Ian Agol, Fernando C. Marques and André Neves, by using Almgren–Pitts min-max theory.〔(【引用サイトリンク】title=() Min-max theory and the energy of links )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Möbius energy」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.