A speed preserving Hilbert gradient flow for generalized integral Menger curvature

DOI10.1515/acv-2021-0037zbMath1526.35352arXiv2103.10408OpenAlexW3154095038WikidataQ114007290 ScholiaQ114007290MaRDI QIDQ6165634

Heiko von der Mosel, Henrik Schumacher, Daniel Steenebrügge, Jan Knappmann

Publication date: 6 July 2023

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.10408

zbMATH Keywords

gradient flowknot energylong-time existence

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (2)

Banach gradient flows for various families of knot energies ⋮ Tangent-point energies and ropelength as gamma-limits of discrete tangent-point energies on biarc curves

Cites Work

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• Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
• Hitchhiker's guide to the fractional Sobolev spaces
• Menger curvature as a knot energy
• On a flow to untangle elastic knots
• The gradient flow of the Möbius energy near local minimizers
• Filling Riemannian manifolds
• Manifolds, tensor analysis, and applications.
• The gradient flow of O'Hara's knot energies
• Sobolev gradients for the Möbius energy
• The gradient flow of the Möbius energy: \(\epsilon\)-regularity and consequences
• On combinatorial isotopy
• Methods of Nonlinear Analysis
• Towards a regularity theory for integral Menger curvature
• Classical Fourier Analysis
• Regularizing and self-avoidance effects of integral Menger curvature
• A simple scheme for the approximation of self-avoiding inextensible curves
• Dynamics of embedded curves by doubly-nonlocal reaction–diffusion systems
• A note on integral Menger curvature for curves
• Knot Tightening by Constrained Gradient Descent
• Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves
• Variational convergence of discrete elasticae

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