Geodesic
A lower bound for the distortion of a knotted curve
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 5-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the distortion of any knotted curve in $\mathbb R^3$ is greater than 4.76. This improves the result by John M. Sullivan and Elizabeth Denne. Bibl. – 3 titles. 
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T. Bereznyak; P. V. Svetlov. A lower bound for the distortion of a knotted curve. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 5-13. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a0/

[1] E. Denne, Y. Diao, J. Sullivan, Quadrisecants give new lower bound for the ropelength of a knot, , 2004 arXiv:math.DG/0408026 | MR

[2] E. Denne, J. Sullivan, The distortion of a knotted curve, , 2004 arXiv:math.GT/0409438 | MR

[3] M. Gromov, “Filling Riemannian Manifolds”, J. Diff. Geom., 18 (1983), 1–147 | MR | Zbl