Torus Knots Extremizing the Möbius Energy

Abstract

Using the principle of symmetric criticality [Palais 1979], we construct torus knots and links that extremize the Möbiusinvariant 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 Mobius energy—applicable to the study of arbitrary knots and links—are also described, and confirm the results of the analytic calculations.

Locations

• Experimental Mathematics - View
• Project Euclid (Cornell University) - View - PDF