Hausdorff dimension of pinned distance sets and the 𝐿²-method

DOI10.1090/proc/14740zbMath1444.28002arXiv1810.08127OpenAlexW2964165874MaRDI QIDQ5206216

Bochen Liu

Publication date: 18 December 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.08127

zbMATH Keywords

Hausdorff dimensionpinned distancesFalconer distance conjecture

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Length, area, volume, other geometric measure theory (28A75)

Related Items

An improvement of the pinned distance set problem in even dimensions ⋮ On the multiparameter Falconer distance problem ⋮ A non-linear version of Bourgain's projection theorem ⋮ Restricted families of projections onto planes: the general case of nonvanishing geodesic curvature ⋮ On the Mattila–Sjölin distance theorem for product sets ⋮ Falconer type functions in three variables ⋮ Structural theorems on the distance sets over finite fields ⋮ Length of sets under restricted families of projections onto lines ⋮ Fourier decay of fractal measures on hyperboloids ⋮ Low-dimensional pinned distance sets via spherical averages ⋮ Improved bounds for the dimensions of planar distance sets ⋮ On Hausdorff dimension of radial projections ⋮ Dimension of divergence set of the wave equation ⋮ Improved bounds for restricted projection families via weighted Fourier restriction

Cites Work

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