Inventiones mathematicae

, Volume 150, Issue 2, pp 257–286

On the minimum ropelength of knots and links

  • Jason Cantarella
  • Robert B. Kusner
  • John M. Sullivan

DOI: 10.1007/s00222-002-0234-y

Cite this article as:
Cantarella, J., Kusner, R. & Sullivan, J. Invent. math. (2002) 150: 257. doi:10.1007/s00222-002-0234-y


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 C1,1 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jason Cantarella
    • 1
  • Robert B. Kusner
    • 2
  • John M. Sullivan
    • 3
  1. 1.Department of Mathematics, University of Georgia, Athens, GA 30602, USA (e-mail:
  2. 2.Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA (e-mail:
  3. 3.Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (e-mail: