Jason Cantarella, Rob Kusner, John M Sullivan
Published 2001-03-30, updated 2002-03-01Version 3
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.
Comments: 29 pages, 14 figures; New version has minor additions and corrections; new section on asymptotic growth of ropelength; several new references
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