Quadrisecants give new lower bounds for the ropelength of a knot

@inproceedings{UANAN2006QuadrisecantsGN,
title={Quadrisecants give new lower bounds for the ropelength of a knot},
author={E LIZABETH D ENNE Y UANAN},
year={2006}
}

E LIZABETH D ENNE Y UANAN

Published 2006

More technically, the thickness τ (K) of a space curve K is defined by Gonzalez and Maddocks [11] to be twice the infimal radius r(a, b, c) of circles through any three distinct points of K . It is known from the work of Cantarella, Kusner and Sullivan [4] that τ (K) = 0 unless K is C1,1 , meaning that its tangent direction is a Lipschitz function of arclength. When K is C1 , we can define normal tubes around K , and then indeed τ (K) is the supremal diameter of such a tube that remains… CONTINUE READING