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On the minimum ropelength of knots and links

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Inventiones mathematicae Aims and scope

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA 30602, USA (e-mail: cantarel@math.uga.edu), , , , , , US

    Jason Cantarella

  2. Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA (e-mail: kusner@math.umass.edu), , , , , , US

    Robert B. Kusner

  3. Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (e-mail: jms@math.uiuc.edu), , , , , , US

    John M. Sullivan

Authors
  1. Jason Cantarella
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  2. Robert B. Kusner
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  3. John M. Sullivan
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Oblatum 11-IV-2001 & 20-III-2002¶Published online: 17 June 2002

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Cantarella, J., Kusner, R. & Sullivan, J. On the minimum ropelength of knots and links. Invent. math. 150, 257–286 (2002). https://doi.org/10.1007/s00222-002-0234-y

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  • DOI: https://doi.org/10.1007/s00222-002-0234-y

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