Symmetric critical knots for O'Hara's energies

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

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