TANGENT-POINT SELF-AVOIDANCE ENERGIES FOR CURVES

DOI10.1142/S0218216511009960zbMath1245.57012arXiv1006.4566MaRDI QIDQ3225660

Heiko von der Mosel, Paweł Strzelecki

Publication date: 22 March 2012

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.4566

zbMATH Keywords

curverectifiableknot typeself-avoidance energy

Mathematics Subject Classification ID

Related Items (19)

Characterizing \(W^{2,p}\) submanifolds by \(p\)-integrability of global curvatures ⋮ Symmetric critical knots for O'Hara's energies ⋮ Tangent-point repulsive potentials for a class of non-smooth \(m\)-dimensional sets in \(\mathbb R^n\). I: smoothing and self-avoidance effects ⋮ On some knot energies involving Menger curvature ⋮ 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 ⋮ Stationary points of O'Hara's knot energies ⋮ Dynamics of embedded curves by doubly-nonlocal reaction–diffusion systems ⋮ Minimal Hölder regularity implying finiteness of integral Menger curvature ⋮ Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds ⋮ Symmetric elastic knots ⋮ Modeling repulsive forces on fibres via knot energies ⋮ Numerical solution of a bending-torsion model for elastic rods ⋮ Mini-workshop: Nonlocal analysis and the geometry of embeddings. Abstracts from the mini-workshop held November 22--28, 2020 (hybrid meeting) ⋮ Menger curvature as a knot energy ⋮ Modeling repulsive forces on fibres via knot energies ⋮ Sobolev gradients for the Möbius energy ⋮ Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves ⋮ THE ENERGY SPACES OF THE TANGENT POINT ENERGIES

Cites Work

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• Characterization of ideal knots
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• What are the longest ropes on the unit sphere?
• On the smoothness of Hölder doubling measures
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• On the minimum ropelength of knots and links
• Euler-Lagrange equations for nonlinearly elastic rods with self-contact
• Global curvature for rectifiable loops
• On rectifiable curves with \(L^{p}\)-bounds on global curvature: self-avoidance, regularity, and minimizing knots
• On Sphere-Filling Ropes
• POLYGONAL KNOT SPACE NEAR ROPELENGTH-MINIMIZED KNOTS
• Global curvature, thickness, and the ideal shapes of knots
• Knot Tightening by Constrained Gradient Descent

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