On a flow to untangle elastic knots

  • Chun-Chi Lin
  • Hartmut R. Schwetlick


In this paper we present a method to untangle smooth knots by a gradient flow for a suitable energy. We show that the flow of smooth initial knots remains smooth for all time and approaches asymptotically an “optimal embedding” in its isotopy type. The method is to set up a gradient flow for the total energy of knots, which consists of bending energy and the Möbius energy of knots.

Mathematics Subject Classification (2000)

35K55 57M25 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan
  2. 2.Department of Mathematical SciencesUniversity of BathBathUK

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