# 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} }

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…

## One Citation

### Tangent-point energies and ropelength as Gamma-limits of discrete tangent-point energies on biarc curves

- MathematicsAdvances in Continuous and Discrete Models
- 2023

Using interpolation with biarc curves we prove Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies in the C1\documentclass[12pt]{minimal} \usepackage{amsmath}…

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