Thickness of knots

DOI10.1016/S0166-8641(97)00210-1zbMath0924.57011OpenAlexW2087704519MaRDI QIDQ1292753

Jonathan K. Simon, Oguz C. Durumeric, Richard A. Litherland, Eric J. Rawdon

Publication date: 24 June 1999

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0166-8641(97)00210-1

zbMATH Keywords

curvaturedistortionedge numberself-distance

Mathematics Subject Classification ID

Related Items (52)

Energy, ropelength, and other physical aspects of equilateral knots. ⋮ Geometric complexity of embeddings in \(\mathbb R^d\) ⋮ Theory of thickened knots ⋮ Shape optimization of self-avoiding curves ⋮ UPPER BOUNDS ON LINKING NUMBERS OF THICK LINKS ⋮ APPROXIMATING SMOOTH THICKNESS ⋮ On rectifiable curves with \(L^{p}\)-bounds on global curvature: self-avoidance, regularity, and minimizing knots ⋮ Total curvature and packing of knots ⋮ Towards a regularity theory for integral Menger curvature ⋮ Can Computers Discover Ideal Knots? ⋮ Minimum lattice length and ropelength of 2-bridge knots and links ⋮ On some knot energies involving Menger curvature ⋮ AVERAGE CROSSING NUMBER, TOTAL CURVATURE AND ROPELENGTH OF THICK KNOTS ⋮ Energy functionals and normal forms of knots and plane curves ⋮ Ribbonlength of families of folded ribbon knots ⋮ Dynamics of embedded curves by doubly-nonlocal reaction–diffusion systems ⋮ POLYGONAL KNOT SPACE NEAR ROPELENGTH-MINIMIZED KNOTS ⋮ Upper bounds for ropelength as a function of crossing number. ⋮ Hamiltonian knot projections and lengths of thick knots. ⋮ Discrete thickness ⋮ Conformal transformations and curvature ⋮ Ribbonlength of folded ribbon unknots in the plane ⋮ Local structure of ideal shapes of knots ⋮ Total curvature and total torsion of knotted random polygons in confinement ⋮ Relative Frequencies of Alternating and Nonalternating Prime Knots and Composite Knots in Random Knot Spaces ⋮ Menger curvature as a knot energy ⋮ Discrete thickness ⋮ THE ADDITIVITY OF CROSSING NUMBERS ⋮ Knot Tightening by Constrained Gradient Descent ⋮ Symmetric criticality for tight knots ⋮ The elastic trefoil is the doubly covered circle ⋮ A celtic framework for knots and links ⋮ ERROR ANALYSIS OF THE MINIMUM DISTANCE ENERGY OF A POLYGONAL KNOT AND THE MÖBIUS ENERGY OF AN APPROXIMATING CURVE ⋮ Total curvature, ropelength and crossing number of thick knots ⋮ THE LOWER BOUNDS OF THE LENGTHS OF THICK KNOTS ⋮ EXISTENCE OF IDEAL KNOTS ⋮ The distortion of a knotted curve ⋮ Ropelength, crossing number and finite-type invariants of links ⋮ Statistical topology of closed curves: Some applications in polymer physics ⋮ HAMILTONIAN CYCLES AND ROPE LENGTHS OF CONWAY ALGEBRAIC KNOTS ⋮ Knots connected by wide ribbons ⋮ Nonuniform thickness and weighted distance ⋮ POLYGONAL APPROXIMATION AND ENERGY OF SMOOTH KNOTS ⋮ The ropelengths of knots are almost linear in terms of their crossing numbers ⋮ The Linear Growth in the Lengths of a Family of Thick Knots ⋮ An Asymptotic Representation Formula for Scattering by Thin Tubular Structures and an Application in Inverse Scattering ⋮ Thickness and crossing number of knots ⋮ Thickness of knots ⋮ Ribbonlength and crossing number for folded ribbon knots ⋮ LOCAL STRUCTURE OF IDEAL KNOTS, II CONSTANT CURVATURE CASE ⋮ Unnamed Item ⋮ Möbius energy of thick knots

Cites Work

• Filling Riemannian manifolds
• Family of energy functionals of knots
• Thickness of knots
• On the total curvature of knots
• AN ELEMENTARY INVARIANT OF KNOTS
• Knot Energies by Ropes
• Non‐recursive functions, knots “with thick ropes,” and self‐clenching “thick” hyperspheres
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