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

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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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     title = {A lower bound for the distortion of a~knotted curve},
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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/