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 
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/
@article{ZNSL_2008_353_a0,
     author = {T. Bereznyak and P. V. Svetlov},
     title = {A lower bound for the distortion of a~knotted curve},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--13},
     year = {2008},
     volume = {353},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a0/}
}
TY  - JOUR
AU  - T. Bereznyak
AU  - P. V. Svetlov
TI  - A lower bound for the distortion of a knotted curve
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2008
SP  - 5
EP  - 13
VL  - 353
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a0/
LA  - en
ID  - ZNSL_2008_353_a0
ER  - 
%0 Journal Article
%A T. Bereznyak
%A P. V. Svetlov
%T A lower bound for the distortion of a knotted curve
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 5-13
%V 353
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a0/
%G en
%F ZNSL_2008_353_a0

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[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