A note on integral Menger curvature for curves

DOI10.1002/mana.201100220zbMath1271.57006OpenAlexW1980892915MaRDI QIDQ4911523

Simon Blatt

Publication date: 15 March 2013

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

Full work available at URL: https://doi.org/10.1002/mana.201100220

zbMATH Keywords

Menger curvatureknot energiesfractional Sobolev spacesgeometric knot theory

Mathematics Subject Classification ID

Related Items (13)

On the analyticity of critical points of the generalized integral Menger curvature in the Hilbert case ⋮ Towards a regularity theory for integral Menger curvature ⋮ A characterisation of inner product spaces by the maximal circumradius of spheres ⋮ On some knot energies involving Menger curvature ⋮ Integral Menger curvature and rectifiability of $n$-dimensional Borel sets in Euclidean $N$-space ⋮ A speed preserving Hilbert gradient flow for generalized integral Menger curvature ⋮ Minimal Hölder regularity implying finiteness of integral Menger curvature ⋮ Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds ⋮ Modeling repulsive forces on fibres via knot energies ⋮ Menger curvature as a knot energy ⋮ Modeling repulsive forces on fibres via knot energies ⋮ Geometric Sobolev-like embedding using high-dimensional Menger-like curvature ⋮ Integro-Differential Harmonic Maps into Spheres

Cites Work

• Unnamed Item
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• Theory of function spaces
• Unrectifiable 1-sets have vanishing analytic capacity
• Menger curvature and rectifiability
• Removable sets for Lipschitz harmonic functions in the plane
• The gradient flow of O'Hara's knot energies
• THE ENERGY SPACES OF THE TANGENT POINT ENERGIES
• BOUNDEDNESS AND REGULARIZING EFFECTS OF O'HARA'S KNOT ENERGIES
• Regularizing and self-avoidance effects of integral Menger curvature

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