On a flow to untangle elastic knots

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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 Mobius energy of knots.
Original languageEnglish
Pages (from-to)621-647
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Issue number3-4
Early online date12 Apr 2010
Publication statusPublished - 1 Nov 2010


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