Approximating Ropelength by Energy Functions

John M Sullivan

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Approximating Ropelength by Energy Functions

John M Sullivan

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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.

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John M Sullivan. 2002-03-20. Approximating Ropelength by Energy Functions. https://arxiv.org/abs/math/0203205

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