On rectifiable curves with \(L^{p}\)-bounds on global curvature: self-avoidance, regularity, and minimizing knots

DOI10.1007/s00209-007-0117-4zbMath1354.49028OpenAlexW2020831090MaRDI QIDQ2384741

Heiko von der Mosel, Paweł Strzelecki

Publication date: 10 October 2007

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0117-4

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Methods involving semicontinuity and convergence; relaxation (49J45) Curves in Euclidean and related spaces (53A04) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

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Cites Work

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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
• Möbius energy of thick knots
• Self-interactions of strands and sheets
• Circles minimize most knot energies
• Sobolev spaces on an arbitrary metric space
• On rectifiable curves with \(L^{p}\)-bounds on global curvature: self-avoidance, regularity, and minimizing knots
• Global curvature for surfaces and area minimization under a thickness constraint
• Menger curvature and $C^{1}$ regularity of fractals
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• ENERGY FUNCTIONS FOR POLYGONAL KNOTS
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