High-dimensional Menger-type curvatures. I: Geometric multipoles and multiscale inequalities
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Publication:2275344
DOI10.4171/RMI/645zbMath1232.28007arXiv0805.1425OpenAlexW3104590871MaRDI QIDQ2275344
Gilad Lerman, J. Tyler Whitehouse
Publication date: 8 August 2011
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0805.1425
Geometric probability and stochastic geometry (60D05) Length, area, volume, other geometric measure theory (28A75) Nontrigonometric harmonic analysis (42C99)
Related Items (19)
Generalized rectifiability of measures and the identification problem ⋮ Characterizing \(W^{2,p}\) submanifolds by \(p\)-integrability of global curvatures ⋮ High-dimensional Menger-type curvatures. II: \(d\)-separation and a menagerie of curvatures ⋮ 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 \(n\)-rectifiability in terms of Jones' square function. II ⋮ Integral Menger curvature and rectifiability of $n$-dimensional Borel sets in Euclidean $N$-space ⋮ Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability ⋮ Sufficient conditions for C^1,α parametrization and rectifiability ⋮ Minimal Hölder regularity implying finiteness of integral Menger curvature ⋮ Sharp boundedness and regularizing effects of the integral Menger curvature for submanifolds ⋮ Symmetrization of a Cauchy-like kernel on curves ⋮ Menger curvature as a knot energy ⋮ Multiscale analysis of 1-rectifiable measures. II: Characterizations ⋮ Foundations of a multi-way spectral clustering framework for hybrid linear modeling ⋮ On \(d\)-dimensional \(d\)-semimetrics and simplex-type inequalities for high-dimensional sine functions ⋮ Characterizations of countably \(n\)-rectifiable Radon measures by higher-dimensional Menger curvatures ⋮ Menger curvatures and \(C^{1,\alpha}\) rectifiability of measures ⋮ Geometric Sobolev-like embedding using high-dimensional Menger-like curvature ⋮ LEAST SQUARES APPROXIMATIONS OF MEASURES VIA GEOMETRIC CONDITION NUMBERS
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