No. 2018.02
Symmetric critical knots for O'Hara's energies
A. Gilsbach and H. von der Mosel
Subject: Knot energy, symmetric criticality, torus knots

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.

Reference

Topology Appl. 242 (2018), 73–102

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arXiv:1709.06949