On the minimum ropelength of knots and links |
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| Authors: | Jason Cantarella Robert B Kusner John M Sullivan |
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| Institution: | (1) Department of Mathematics, University of Georgia, Athens, GA 30602, USA (e-mail: cantarel@math.uga.edu), US;(2) Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA (e-mail: kusner@math.umass.edu), US;(3) Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (e-mail: jms@math.uiuc.edu), US |
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| Abstract: | The ropelength of a knot is the quotient of its length by 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.
Oblatum 11-IV-2001 & 20-III-2002?Published online: 17 June 2002 |
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