On the geometry of stiff knots

  • O. Pierre-Louis
Interdisciplinary Physics


We analyse the geometry of a thin knotted string with bending rigidity. Two types of geometric properties are investigated. First, following the approach of von der Mosel [H. von der Mosel, Asymptotic Anal. 18, 49 (1998)], we derive upper bounds for the multiplicity of crossings and braids. Then, using a general inequality for the length of 3D curves derived by Chakerian [G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)], we analyze the size and confinement of a knot


46.70.Hg Membranes, rods, and strings 02.10.Kn Knot theory 47.57.Ng Polymers and polymer solutions 87.14.gk DNA 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Laboratoire de Spectrométrie Physique, CNRS Univ. J. FourierSaint Martin d’HèresFrance
  2. 2.Rudolf Peierls Centre for Theoretical PhysicsOxfordUK

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