On the Minimum Ropelength of Knots and Links
Jason Cantarella, Rob Kusner, John M Sullivan
Abstract
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 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.
Create a lesson
Related papers
h-cobordisms between 1-connected manifolds with boundary
Ansel Goh
Scalar curvature, volume, and Weil-Petersson translation length
Cameron Gates Rudd
Holomorphic Triangles in the Heegaard Floer Pillowcase
Eaman Eftekhary, Marzieh Souri
Random Quotients of Hyperbolic Spaces with Respect to WPD Actions and Linear Connectivity of the Boundary
Inhyeok Choi, Henry Talbott
Exotic diffeomorphisms on closed aspherical 4-manifolds
Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee et al.
A counterexample to a conjecture of Plotnick on knot exteriors
Tommy Hofmann, John Nicholson