TY - JOUR
T1 - On a flow to untangle elastic knots
AU - Lin, Chun Chi
AU - Schwetlick, Hartmut R.
N1 - Funding Information:
The work in this article was partially supported by Taiwan National Science Council Grant 96-2115-M-003-008.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-010-0328-0
DO - 10.1007/s00526-010-0328-0
M3 - Article
AN - SCOPUS:77957996837
SN - 0944-2669
VL - 39
SP - 621
EP - 647
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
ER -