Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)

Abstract

We prove that if a curve parametrized by arc length is a stationary point of the Moebius energy introduced by Jun O'Hara, then it is smooth whenever the Moebius energy is finite. Our methods, interestingly, only rely on purely analytical arguments, entirely without using Moebius invariance. Furthermore, the techniques involved are not fundamentally restricted to one-dimensional domains, but are generalizable to arbitrary dimensions.

removed minor flaws, changed notation, smashier title

References in corpus (4)

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• 3-Commutators Estimates and the Regularity of 1/2 Harmonic Maps into Spheres
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• On regularity theory for n/p-harmonic maps into manifolds
• Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension
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• Dynamics of Embedded Curves by Doubly-Nonlocal Reaction-Diffusion Systems
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• On the regularity of critical points for O'Hara's knot energies: From smoothness to analyticity
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• Three examples of Sharp Commutator Estimates via Harmonic Extensions
• Möbius invariant metrics on the space of knots
• Variational formulae and estimates of O'Hara's knot energies
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• M{ö}bius-invariant self-avoidance energies for non-smooth sets in arbitrary dimensions