Characterization of rectifiable measures in terms of 𝛼-numbers
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Publication:5130412
DOI10.1090/tran/8170zbMath1454.28001arXiv1808.07661OpenAlexW3016283486MaRDI QIDQ5130412
Jonas Azzam, Xavier Tolsa, Tatiana Toro
Publication date: 4 November 2020
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1808.07661
Wasserstein distancerectifiable setsJones' \(\beta\)-numbersrectifiable measuresJones' \(\alpha\)-numbers
Contents, measures, outer measures, capacities (28A12) Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78)
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Cites Work
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- Multiscale analysis of 1-rectifiable measures. II: Characterizations
- Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
- Characterization of \(n\)-rectifiability in terms of Jones' square function. II
- Menger curvature and rectifiability
- Absolute continuity and \({\alpha}\)-numbers on the real line
- Boundedness of the density normalised Jones' square function does not imply 1-rectifiability
- A differentiable structure for metric measure spaces
- Effective Reifenberg theorems in Hilbert and Banach spaces
- Rectifiability of measures and the \(\beta_p\) coefficients
- Multiscale analysis of 1-rectifiable measures: necessary conditions
- Rectifiable sets, densities and tangent measures
- A characterization of 1-rectifiable doubling measures with connected supports
- Wasserstein distance and the rectifiability of doubling measures. I
- Two sufficient conditions for rectifiable measures
- Sets of Finite Perimeter and Geometric Variational Problems
- Reifenberg parameterizations for sets with holes
- A doubling measure on $\mathbb {R}^d$ can charge a rectifiable curve
- Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality
- Conditions quantitatives de rectifiabilité
- Quantifying curvelike structures of measures by usingL2 Jones quantities
- Rectifiability via a Square Function and Preiss’ Theorem
- Rectifiable measures, square functions involving densities, and the Cauchy transform
- Characterization of \(n\)-rectifiability in terms of Jones' square function. I
