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MiS Preprint

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

Simon Blatt, Armin Schikorra and Philipp Reiter


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.

Aug 2, 2012
Aug 13, 2012
MSC Codes:
57M25, 46E35

Related publications

2016 Repository Open Access
Simon Blatt, Philipp Reiter and Armin Schikorra

Harmonic analysis meets critical knots : critical points of the Möbius energy are smooth

In: Transactions of the American Mathematical Society, 368 (2016) 9, pp. 6391-6438