On the minimum ropelength of knots and links

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.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Oblatum 11-IV-2001 & 20-III-2002¶Published online: 17 June 2002

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Keywords

  • Link Type
  • Normal Tube