A doubling measure on $\mathbb {R}^d$ can charge a rectifiable curve
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Publication:3558998
DOI10.1090/S0002-9939-10-10234-2zbMath1196.28007arXiv0906.2484OpenAlexW1602675159MaRDI QIDQ3558998
Raanan Schul, Rowan Killip, John B. Garnett
Publication date: 11 May 2010
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0906.2484
Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Length, area, volume, other geometric measure theory (28A75)
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Generalized rectifiability of measures and the identification problem ⋮ A \(T1\) theorem for general Calderón-Zygmund operators with comparable doubling weights, and optimal cancellation conditions ⋮ Geometry of measures in real dimensions via Hölder parameterizations ⋮ Lipschitz functions with prescribed blowups at many points ⋮ Boundedness of the density normalised Jones' square function does not imply 1-rectifiability ⋮ Zygmund graphs are thin for doubling measures ⋮ Identifying 1-rectifiable measures in Carnot groups ⋮ Sufficient conditions for C^1,α parametrization and rectifiability ⋮ Characterization of rectifiable measures in terms of 𝛼-numbers ⋮ Rigidity of derivations in the plane and in metric measure spaces ⋮ Integral energy characterization of Hajłasz-Sobolev spaces ⋮ Multiscale analysis of 1-rectifiable measures. II: Characterizations ⋮ A function whose graph has positive doubling measure ⋮ Bi-Lipschitz parts of quasisymmetric mappings ⋮ Two sufficient conditions for rectifiable measures ⋮ Sufficient condition for rectifiability involving Wasserstein distance \(W_2\) ⋮ On thin carpets for doubling measures ⋮ Effective Reifenberg theorems in Hilbert and Banach spaces ⋮ Normal numbers are not fat for doubling measures ⋮ Hölder coverings of sets of small dimension ⋮ Radon measures and Lipschitz graphs ⋮ Multiscale analysis of 1-rectifiable measures: necessary conditions
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