35 citations · 72 across the 15 of their papers we have counts for
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math.GT2004★ 5 cited
The Distortion of a Knotted Curve
Elizabeth Denne, John M Sullivan
The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we…
math.GT2004★ 35 cited
Quadrisecants give new lower bounds for the ropelength of a knot
Elizabeth Denne, Yuanan Diao, John M Sullivan
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical…