• Corpus ID: 248426922

Banach gradient flows for various families of knot energies

@inproceedings{Matt2022BanachGF,
  title={Banach gradient flows for various families of knot energies},
  author={Hannes Matt and Daniel Steenebrugge and Heiko von der Mosel},
  year={2022}
}

• Hannes Matt, Daniel Steenebrugge, H. Mosel
• Published 28 April 2022
• Mathematics

We establish long-time existence of Banach gradient flows for generalised integral Menger curvatures and tangent-point energies, and for O’Hara’s self-repulsive potentials E α,p . In order to do so, we employ the theory of curves of maximal slope in slightly smaller spaces compactly embedding into the respective energy spaces associated to these functionals, and add a term involving the logarithmic strain, which controls the parametrisations of the flowing (knotted) loops. As a prerequisite, we prove in addition that O’Hara’s knot energies E α,p are continuously differentiable.