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.
|Number of pages||27|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2010 Apr 13|
ASJC Scopus subject areas
- Applied Mathematics