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

By Simon Blatt, Philipp Reiter, Armin Schikorra. 2012

53 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6fef69400a9a0d70abb20b04ab52c875796730f0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. E. Lenzmann
2. Armin Schikorra
3. Katarzyna Mazowiecka
4. Giampiero Palatucci

In Geometry and Topology

1. E. Lenzmann
2. Armin Schikorra

Citations in the corpus

• Sharp commutator estimates via harmonic extensions (2016, background): “the ones introduced by the second-named author in [36], see also [18, 2, 40].”