Möbius invariance of knot energy
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- by Steve Bryson, Michael H. Freedman, Zheng-Xu He and Zhenghan Wang PDF
- Bull. Amer. Math. Soc. 28 (1993), 99-103 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 28 (1993), 99-103
- MSC: Primary 57M25; Secondary 57N45, 58E10
- DOI: https://doi.org/10.1090/S0273-0979-1993-00348-3
- MathSciNet review: 1168514