Approximating Ropelength by Energy Functions

Details Approximating Ropelength by Energy Functions Approximating Ropelength by Energy Functions

2002-03-20

arxiv.org/abs/math/0203205v1

Mathematics

Geometric Topology

6 pages, 2 figures, LaTeX

Scientific paper

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.

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