Approximating Ropelength by Energy Functions
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
The ropelength of a knot is the quotient of its length by its thickness. We consider a family of energy functions for knots, depending on a power p, which approach ropelength as p increases. We describe a numerically computed trefoil knot which seems to be a local minimum for ropelength; there are nearby critical points for the p-energies, which are evidently local minima for large enough p.
Cite
@article{arxiv.math/0203205,
title = {Approximating Ropelength by Energy Functions},
author = {John M Sullivan},
journal= {arXiv preprint arXiv:math/0203205},
year = {2007}
}
Comments
6 pages, 2 figures, LaTeX