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arXiv · 1709.06949

Symmetric critical knots for O'Hara's energies

Alexandra Gilsbach·Heiko von der Mosel
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Abstract

We prove the existence of symmetric critical torus knots for O'Hara's knot energy family $E_\alpha$, $\alpha\in (2,3)$ using Palais' classic principle of symmetric criticality. It turns out that in every torus knot class there are at least two smooth $E_\alpha$-critical knots, which supports experimental observations using numerical gradient flows.

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Alexandra Gilsbach, Heiko von der Mosel. 2017-09-20. Symmetric critical knots for O'Hara's energies. https://doi.org/10.1016/j.topol.2018.04.014

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