Approximating Ropelength by Energy Functions

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 n...

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Bibliographic Details
Published inarXiv.org
Main Author Sullivan, John M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.03.2002
Subjects
Critical point
Knots
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Summary: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.
ISSN:2331-8422