Slices and distances: on two problems of Furstenberg and Falconer
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Publication:6119195
DOI10.4171/icm2022/97arXiv2109.12157OpenAlexW3202464183MaRDI QIDQ6119195
Publication date: 22 March 2024
Published in: International Congress of Mathematicians (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.12157
Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45) Extremal combinatorics (05D99)
Cites Work
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- Local entropy averages and projections of fractal measures
- On the Erdős distinct distances problem in the plane
- On the distance sets of Ahlfors-David regular sets
- The discretized sum-product and projection theorems
- On self-similar sets with overlaps and inverse theorems for entropy
- Orthogonal projections of discretized sets
- Multifractal measures and a weak separation condition
- Hausdorff dimension and distance sets
- On the dimension and smoothness of radial projections
- On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions
- An \(L^2\)-identity and pinned distance problem
- Convolutions of Cantor measures without resonance
- On measures that improve \(L^q\) dimension under convolution
- New bounds on the dimensions of planar distance sets
- Digit expansions of numbers in different bases
- Improved bounds for the dimensions of planar distance sets
- An improved result for Falconer's distance set problem in even dimensions
- A new dynamical proof of the Shmerkin-Wu theorem
- On arithmetic sums of Ahlfors-regular sets
- On Falconer's distance set problem in the plane
- A proof of Furstenberg's conjecture on the intersections of \(\times p\)- and \(\times q\)-invariant sets
- Sharp \(L^2\) estimates of the Schrödinger maximal function in higher dimensions
- On the dimension of Bernoulli convolutions for all transcendental parameters
- On the Hausdorff dimension of pinned distance sets
- On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
- On the Erdős-Volkmann and Katz-Tao ring conjectures
- Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus
- Resonance between Cantor sets
- On the Hausdorff dimensions of distance sets
- Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets
- Borel subrings of the reals
- An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³
- On the Assouad dimension of projections
- An improvement on Furstenberg’s intersection problem
- On the Discretized Sum-Product Problem
- Slicing theorems and rigidity phenomena for self‐affine carpets
- DIMENSION THEORY OF SELF-SIMILAR SETS AND MEASURES
- Ergodic fractal measures and dimension conservation
- Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
- On Hausdorff dimension of projections
- Weighted restriction estimates and application to Falconer distance set problem
- Some connections between Falconer's distance set conjecture and sets of Furstenburg type
- A non-linear version of Bourgain's projection theorem
