Möbius invariance of knot energy
Steve Bryson, Michael Hartley Freedman, Zheng-Xu He, Zhenghan Wang · arXiv (Cornell University) · 1993
A physically natural potential energy for simple closed curves in $\bold R^3$ 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.