On the Minimum Ropelength of Knots and Links

Abstract

The ropelength of a knot is the quotient of its length and its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are $C^{1,1}$ curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.

29 pages, 14 figures; New version has minor additions and corrections; new section on asymptotic growth of ropelength; several new references

References in corpus (2)

• Higher-Order Polynomial Invariants of 3-Manifolds Giving Lower Bounds for the Thurston Norm
• On Distortion and Thickness of Knots

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• Analysis of the first variation and a numerical gradient flow for integral Menger curvature
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• Higher-Order Polynomial Invariants of 3-Manifolds Giving Lower Bounds for the Thurston Norm
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