On a flow to untangle elastic knots

Chun-Chi Lin, Hartmut R. Schwetlick

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)621-647
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Volume39
Issue number3
DOIs
Publication statusPublished - 2010 Apr 13

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Knot
Gradient Flow
Energy
Isotopy

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On a flow to untangle elastic knots. / Lin, Chun-Chi; Schwetlick, Hartmut R.

In: Calculus of Variations and Partial Differential Equations, Vol. 39, No. 3, 13.04.2010, p. 621-647.

Research output: Contribution to journalArticle

Lin, Chun-Chi ; Schwetlick, Hartmut R. / On a flow to untangle elastic knots. In: Calculus of Variations and Partial Differential Equations. 2010 ; Vol. 39, No. 3. pp. 621-647.
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