Hausdorff dimension, intersections of projections and exceptional plane sections

DOI10.1090/proc/12985zbMath1345.28008arXiv1509.05724OpenAlexW3105616327WikidataQ109996585 ScholiaQ109996585MaRDI QIDQ2809197

Tuomas Orponen, Pertti Mattila

Publication date: 27 May 2016

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

Full work available at URL: https://arxiv.org/abs/1509.05724

zbMATH Keywords

Hausdorff dimensionorthogonal projectionplane section

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75)

Related Items (15)

Hausdorff dimension of intersections with planes and general sets ⋮ On arithmetic sums of Ahlfors-regular sets ⋮ Hausdorff Dimension Exceptional Set Estimates for Projections, Sections and Intersections ⋮ On the multiparameter Falconer distance problem ⋮ On the Hausdorff dimension of pinned distance sets ⋮ A sharp exceptional set estimate for visibility ⋮ Projections in vector spaces over finite fields ⋮ On the dimension and smoothness of radial projections ⋮ Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets ⋮ A large plane set intersecting lines in infinitely many directions in at most one point ⋮ On distance sets, box-counting and Ahlfors-regular sets ⋮ Intersections of projections and slicing theorems for the isotropic Grassmannian and the Heisenberg group ⋮ New bounds on the dimensions of planar distance sets ⋮ On Hausdorff dimension of radial projections ⋮ An improved bound on the packing dimension of Furstenberg sets in the plane

Cites Work

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• Slicing sets and measures, and the dimension of exceptional parameters
• Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
• Hausdorff dimension, orthogonal projections and intersections with planes
• Convolutions and the Geometry of Multifractal Measures
• Measure and dimension functions: measurability and densities
• Fourier Analysis and Hausdorff Dimension
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions

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