Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Torus Knots Extremizing the Möbius Energy

D. Kim
R. Kusner
Journal / Anthology

Experimental Mathematics
Year: 1993
Volume: 2
Issue: 1
Page range: 1-9

Using the principle of symmetric criticality [Palais 1979], we construct torus knots and links that extremize the Möbius-invariant energy introduced by O'Hara [1991] and Freedman, He and Wang [1993]. The critical energies are explicitly computable using the calculus of residues, a result obtained in collaboration with Gil Stengle. Experiments with a discretized version of the Möbius energy--applicable to the study of arbitrary knots and links--are also described, and confirm the results of the analytic calculations.

*Mathematics > Topology