Torus Knots Extremizing the Möbius Energy
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 2 (1) , 1-9
- https://doi.org/10.1080/10586458.1993.10504264
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.Keywords
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