On restricted families of projections in ℝ3

DOI10.1112/plms/pdu004zbMath1302.28015arXiv1302.6550OpenAlexW2114357685WikidataQ109996593 ScholiaQ109996593MaRDI QIDQ2921105

Tuomas Orponen, Katrin S. Fässler

Publication date: 30 September 2014

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

Full work available at URL: https://arxiv.org/abs/1302.6550

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (22)

Dimension distortion by right coset projections in the Heisenberg group ⋮ Orthogonal projections of discretized sets ⋮ Projections of planar sets in well-separated directions ⋮ An improved bound for the dimension of \((\alpha,2\alpha)\)-Furstenberg sets ⋮ Distance sets, orthogonal projections and passing to weak tangents ⋮ On the packing dimension of Furstenberg sets ⋮ Dimension estimates on circular (s,t)-Furstenberg sets ⋮ Restricted families of projections onto planes: the general case of nonvanishing geodesic curvature ⋮ Projection theorems for linear-fractional families of projections ⋮ An exceptional set estimate for restricted projections to lines in \(\mathbb{R}^3\) ⋮ On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane ⋮ Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem ⋮ Length of sets under restricted families of projections onto lines ⋮ Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets ⋮ Projection theorems in hyperbolic space ⋮ Application of a Fourier restriction theorem to certain families of projections in \(\mathbb R^3\) ⋮ Combinatorial proofs of two theorems of Lutz and Stull ⋮ Hausdorff dimension estimates for restricted families of projections in \(\mathbb{R}^3\) ⋮ Sixty Years of Fractal Projections ⋮ An improved bound on the packing dimension of Furstenberg sets in the plane ⋮ Hausdorff dimension and projections related to intersections ⋮ Improved bounds for restricted projection families via weighted Fourier restriction

Cites Work

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• Application of a Fourier restriction theorem to certain families of projections in \(\mathbb R^3\)
• Hilbert transforms along curves. I: Nilpotent groups
• Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions
• On the distance sets of self-similar sets
• Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets
• Hausdorff dimension, orthogonal projections and intersections with planes
• Hausdorff dimension and exceptional sets of linear transformations
• Self-similar measures and intersections of Cantor sets
• One-dimensional families of projections
• On Hausdorff dimension of projections
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions

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