Miura's second-energy conjecture for the elastic propeller
Miura's second-energy conjecture for the elastic propeller
For a tame knot class , let be the -closure of the class of unit-length, arclength-parametrized closed curves in :
A stable elastic knot for is a curve that locally minimizes the bending energy on a connected component of the knot class, and it is strictly stable if the minimum is strict up to isometry. Elastic propeller conjecture. The elastic propeller is a strictly stable elastic knot for the unknot class. Moreover, among all stable elastic knots for the unknot class, it has the second smallest energy. The circle is the least-energy stable elastic unknot, so the conjecture identifies the elastic propeller as the next energy level. The source attributes this conjecture to Miura; its resolution is not specified.
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Sources & referencesView supporting material
Primary source
Tatsuya Miura, “Elastic curves and self-intersections”, arXiv:2408.03020 (2025).
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