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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Möbius invariance of knot energy


Authors: Steve Bryson, Michael H. Freedman, Zheng-Xu He and Zhenghan Wang
Journal: Bull. Amer. Math. Soc. 28 (1993), 99-103
MSC: Primary 57M25; Secondary 57N45, 58E10
MathSciNet review: 1168514
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Abstract: A physically natural potential energy for simple closed curves in $ {\textbf{R}}^{3}$ is shown to be invariant under Möbius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute minima for energy; there is a minimum energy threshold below which knotting cannot occur; minimizers within prime knot types exist and are regular. Finally, the number of knot types with energy less than any constant M is estimated.


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DOI: http://dx.doi.org/10.1090/S0273-0979-1993-00348-3
PII: S 0273-0979(1993)00348-3
Article copyright: © Copyright 1993 American Mathematical Society