Tangent-point repulsive potentials for a class of non-smooth \(m\)-dimensional sets in \(\mathbb R^n\). I: smoothing and self-avoidance effects

DOI10.1007/s12220-011-9275-zzbMath1285.53004arXiv1102.3642OpenAlexW2102905331MaRDI QIDQ363200

Paweł Strzelecki, Heiko von der Mosel

Publication date: 2 September 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.3642

zbMATH Keywords

curvature energiesgeometric Sobolev-Morrey theoremnon-smooth setsrepulsive potentials

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (16)

Shape optimization of self-avoiding curves ⋮ Tangent-point repulsive potentials for a class of non-smooth \(m\)-dimensional sets in \(\mathbb R^n\). I: smoothing and self-avoidance effects ⋮ Simulating Self-Avoiding Isometric Plate Bending ⋮ On some knot energies involving Menger curvature ⋮ Self‐repulsiveness of energies for closed submanifolds ⋮ Möbius-invariant self-avoidance energies for non-smooth sets of arbitrary dimension and co-dimension ⋮ Integral Menger curvature and rectifiability of $n$-dimensional Borel sets in Euclidean $N$-space ⋮ A descent scheme for thick elastic curves with self-contact and container constraints ⋮ Mathematical imaging and surface processing. Abstracts from the workshop held August 21--27, 2022 ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ Minimal Hölder regularity implying finiteness of integral Menger curvature ⋮ 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 ⋮ Limits of conformal immersions under a bound on a fractional normal curvature quantity ⋮ Sobolev gradients for the Möbius energy ⋮ Geometric Sobolev-like embedding using high-dimensional Menger-like curvature

Cites Work

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• Tangent-point repulsive potentials for a class of non-smooth \(m\)-dimensional sets in \(\mathbb R^n\). I: smoothing and self-avoidance effects
• Characterization of ideal knots
• Regularity theory for the Möbius energy
• Integral Menger curvature for surfaces
• What are the longest ropes on the unit sphere?
• High-dimensional Menger-type curvatures. II: \(d\)-separation and a menagerie of curvatures
• On the smoothness of Hölder doubling measures
• Rectifiability, analytic capacity, and singular integrals
• Analytic capacity, Calderón-Zygmund operators, and rectifiability
• Menger curvature and rectifiability
• Möbius energy of knots and unknots
• Global curvature and self-contact of nonlinearly elastic curves and rods
• On the minimum ropelength of knots and links
• Euler-Lagrange equations for nonlinearly elastic rods with self-contact
• Global curvature for rectifiable loops
• Self-interactions of strands and sheets
• Existence of surfaces minimizing the Willmore functional
• High-dimensional Menger-type curvatures. I: Geometric multipoles and multiscale inequalities
• Global curvature for surfaces and area minimization under a thickness constraint
• On the first variation of a varifold
• Repulsive knot energies and pseudodifferential calculus for O’Hara’s knot energy family E ^(α) , α ∈ [2, 3)
• On Sphere-Filling Ropes
• TANGENT-POINT SELF-AVOIDANCE ENERGIES FOR CURVES
• Regularizing and self-avoidance effects of integral Menger curvature
• Differential Topology
• Mean curvature flow and geometric inequalities
• Global curvature, thickness, and the ideal shapes of knots
• Chord-arc constants for submanifolds of arbitrary codimension

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