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arXiv · 2204.13603

Banach gradient flows for various families of knot energies

Hannes Matt·Daniel Steenebrügge·Heiko von der Mosel
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Abstract

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 $E^{\alpha,p}$. 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 $E^{\alpha,p}$ are continuously differentiable.

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Hannes Matt, Daniel Steenebrügge, Heiko von der Mosel. 2022-04-28. Banach gradient flows for various families of knot energies. https://doi.org/10.1007/s00028-022-00863-x

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