Orthogonal projections of discretized sets

DOI10.4171/JFG/92zbMath1455.28007arXiv1710.00795MaRDI QIDQ826449

Weikun He

Publication date: 4 January 2021

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

Full work available at URL: https://arxiv.org/abs/1710.00795

zbMATH Keywords

Hausdorff dimensionprojection theoremdiscretized set

Mathematics Subject Classification ID

Fractals (28A80) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (11)

Linear random walks on the torus ⋮ An improved bound for the dimension of \((\alpha,2\alpha)\)-Furstenberg sets ⋮ Hausdorff Dimension Exceptional Set Estimates for Projections, Sections and Intersections ⋮ On the packing dimension of Furstenberg sets ⋮ A non-linear version of Bourgain's projection theorem ⋮ Vertical projections in the Heisenberg group via cinematic functions and point-plate incidences ⋮ On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane ⋮ Slices and distances: on two problems of Furstenberg and Falconer ⋮ A capacity approach to box and packing dimensions of projections of sets and exceptional directions ⋮ Discretized sum-product and Fourier decay in \(\mathbb{R}^n\) ⋮ Discretized sum-product estimates in matrix algebras

Cites Work

• Unnamed Item
• Hausdorff dimension and non-degenerate families of projections
• The discretized sum-product and projection theorems
• Restricted families of projections and random subspaces
• Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
• Hausdorff dimension estimates for restricted families of projections in \(\mathbb{R}^3\)
• Discretized sum-product estimates in matrix algebras
• Exponential sum estimates over a subgroup in an arbitrary finite field
• Product set estimates for non-commutative groups
• On covering numbers of sublevel sets of analytic functions
• Sixty Years of Fractal Projections
• On restricted families of projections in ℝ³
• Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus
• Restricted Radon Transforms and Projections of Planar Sets
• Hausdorff dimension and the exceptional set of projections
• Hausdorff dimension, orthogonal projections and intersections with planes
• Projections of Bodies and Hereditary Properties of Hypergraphs
• Fourier Analysis and Hausdorff Dimension
• One-dimensional families of projections
• An inequality related to the isoperimetric inequality

This page was built for publication: Orthogonal projections of discretized sets