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

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