REVIEW 5 cited by
Furstenberg sets estimate in the plane
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We fully resolve the Furstenberg set conjecture in $\mathbb{R}^2$, that a $(s, t)$-Furstenberg set has Hausdorff dimension $\ge \min(s+t, \frac{3s+t}{2}, s+1)$. As a result, we obtain an analogue of Elekes' bound for the discretized sum-product problem and resolve an orthogonal projection question of Oberlin.
Forward citations
Cited by 5 Pith papers
-
Projections of self-affine sets onto lines
Under strong pinching and strong irreducibility of the linear parts, every line projection of a self-affine set attains the expected dimension; in the plane, strong irreducibility alone suffices.
-
Algorithmic Information Bounds for Distances and Orthogonal Projections
A new proof technique shows distances and orthogonal projections retain at least half of a planar point's Kolmogorov complexity, improving pinned distance dimension bounds to 3/4 s and generalizing Bourgain's theorem.
-
Furstenberg set theorem for transversal families of functions
A sharp dimension bound for Furstenberg sets built from transversal families of graphs, with an application to Fourier decay of fractal measures on convex curves.
-
Two-ends Furstenberg inequality for transversal families and applications to Fourier decay
A simplified two-ends Furstenberg inequality holds for transversal curve families and yields L6 Fourier decay R^{2-5s/2+ε} for s-Frostman measures on convex curves when s≤2/3.
-
Applications of dimension interpolation to orthogonal projections
This survey shows how the Assouad spectrum, intermediate dimensions, and Fourier spectrum yield sharper projection theorems for fractal sets.
Discussion (0). Continue with ORCID to comment.