Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds

DOI10.1016/j.aim.2012.03.007zbMath1246.53005arXiv1110.4786OpenAlexW1987491130MaRDI QIDQ438164

Simon Blatt, Sławomir Kolasiński

Publication date: 20 July 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4786

zbMATH Keywords

Menger curvatureregularity theorySobolev-Slobodeckij spaces

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) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75)

Related Items (12)

Characterizing \(W^{2,p}\) submanifolds by \(p\)-integrability of global curvatures ⋮ On the analyticity of critical points of the generalized integral Menger curvature in the Hilbert case ⋮ Towards a regularity theory for integral Menger curvature ⋮ 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 ⋮ Sufficient conditions for C^1,α parametrization and rectifiability ⋮ Minimal Hölder regularity implying finiteness of integral Menger curvature ⋮ Menger curvature as a knot energy ⋮ Menger curvatures and \(C^{1,\alpha}\) rectifiability of measures ⋮ Geometric Sobolev-like embedding using high-dimensional Menger-like curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Integral Menger curvature for surfaces
• High-dimensional Menger-type curvatures. II: \(d\)-separation and a menagerie of curvatures
• Rectifiability, analytic capacity, and singular integrals
• Unrectifiable 1-sets have vanishing analytic capacity
• Menger curvature and rectifiability
• High-dimensional Menger-type curvatures. I: Geometric multipoles and multiscale inequalities
• On rectifiable curves with \(L^{p}\)-bounds on global curvature: self-avoidance, regularity, and minimizing knots
• TANGENT-POINT SELF-AVOIDANCE ENERGIES FOR CURVES
• Global curvature, thickness, and the ideal shapes of knots
• A note on integral Menger curvature for curves

This page was built for publication: Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds