Improved bounds for the dimensions of planar distance sets

DOI10.4171/JFG/97zbMath1467.28004arXiv1811.03379MaRDI QIDQ2031472

Pablo Shmerkin

Publication date: 9 June 2021

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.03379

zbMATH Keywords

Hausdorff dimensionbox counting dimensiondistance setsFalconer's problempinned distance sets

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)

Related Items (11)

An improvement of the pinned distance set problem in even dimensions ⋮ Finite point configurations and the regular value theorem in a fractal setting ⋮ On the multiparameter Falconer distance problem ⋮ A non-linear version of Bourgain's projection theorem ⋮ On the Mattila–Sjölin distance theorem for product sets ⋮ Slices and distances: on two problems of Furstenberg and Falconer ⋮ Structural theorems on the distance sets over finite fields ⋮ An \(L^2\)-identity and pinned distance problem ⋮ Low-dimensional pinned distance sets via spherical averages ⋮ Unnamed Item ⋮ On Hausdorff dimension of radial projections

Cites Work

• Unnamed Item
• On the dimension and smoothness of radial projections
• An \(L^2\)-identity and pinned distance problem
• New bounds on the dimensions of planar distance sets
• On Falconer's distance set problem in the plane
• Sharp \(L^2\) estimates of the Schrödinger maximal function in higher dimensions
• On the Hausdorff dimension of pinned distance sets
• Pinned distance problem, slicing measures, and local smoothing estimates
• On the Hausdorff dimensions of distance sets
• Hausdorff dimension of pinned distance sets and the 𝐿²-method
• Weighted restriction estimates and application to Falconer distance set problem

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