Freedman, Michael H.; He, Zheng-Xu; Wang, Zhenghan Möbius energy of knots and unknots. (English) Zbl 0817.57011 Ann. Math. (2) 139, No. 1, 1-50 (1994). The authors prove: – the Möbius invariance of the energy of a simple closed curve in \(\mathbb{R}^ 3\) and that the energy bounds the average crossing number of curves in \(\mathbb{R}^ 3\); – the existence of curves which minimize the energy in the family of loops representing any given irreducible knot; – curves of finite energy are topologically tame and – variational formulas for the gradient of the energy. Reviewer: I.Mihuţ (Timişoara) Cited in 10 ReviewsCited in 96 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 58E99 Variational problems in infinite-dimensional spaces 53A04 Curves in Euclidean and related spaces Keywords:Möbius invariance; energy of a simple closed curve in \(\mathbb{R}^ 3\); average crossing number; curves which minimize the energy; topologically tame; gradient of the energy PDFBibTeX XMLCite \textit{M. H. Freedman} et al., Ann. Math. (2) 139, No. 1, 1--50 (1994; Zbl 0817.57011) Full Text: DOI