%0 Journal Article
%T M£¿bius invariance of knot energy
%A Steve Bryson
%A Michael H. Freedman
%A Zheng-Xu He
%A Zhenghan Wang
%J Mathematics
%D 1993
%I arXiv
%X A physically natural potential energy for simple closed curves in $\bold R^3$ is shown to be invariant under M\"obius 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.
%U http://arxiv.org/abs/math/9301212v1