Abstract
AbstractMinimizing the bending energy within knot classes leads to the concept of elastic knots which has been initiated by von der Mosel (Asymptot Anal 18(1–2):49–65, 1998). Motivated by numerical experiments in Bartels and Reiter (Math Comput 90(330):1499–1526, 2021) we prescribe dihedral symmetry and establish existence of dihedrally symmetric elastic knots for knot classes admitting this type of symmetry. Among other results we prove that the dihedral elastic trefoil is the union of two circles that form a (planar) figure-eight. We also discuss some generalizations and limitations regarding other symmetries and knot classes.
Funder
Japan Society for the Promotion of Science
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
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