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.
|Number of pages||27|
|Journal||Calculus of Variations and Partial Differential Equations|
|Early online date||12 Apr 2010|
|Publication status||Published - 1 Nov 2010|