Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem
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Publication:6657474
DOI10.2140/APDE.2025.18.265MaRDI QIDQ6657474
Publication date: 6 January 2025
Published in: Analysis \& PDE (Search for Journal in Brave)
projectionsHausdorff dimensionFurstenberg setssum-productincidencesdiscretized setsBourgain's projection theorem
Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Hausdorff and packing measures (28A78)
Cites Work
- Title not available (Why is that?)
- The discretized sum-product and projection theorems
- An improved bound for the dimension of \((\alpha,2\alpha)\)-Furstenberg sets
- On the packing dimension of Furstenberg sets
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- Bounding the dimension of points on a line
- On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
- On the Erdős-Volkmann and Katz-Tao ring conjectures
- Furstenberg sets for a fractal set of directions
- On restricted families of projections in \(\mathbb{R}^{3}\)
- On the number of sums and products
- Some toy Furstenberg sets and projections of the four-corner Cantor set
- Some connections between Falconer's distance set conjecture and sets of Furstenburg type
- A non-linear version of Bourgain's projection theorem
- 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
- Incidence estimates for \(\alpha \)-dimensional tubes and \(\beta \)-dimensional balls in \(\mathbb{R}^2\)
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