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 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

Article copyright:
© Copyright 1993
American Mathematical Society