Furstenberg sets estimate in the plane
Kevin Ren, Hong Wang

TL;DR
This paper proves the Furstenberg set conjecture in the plane, establishing precise lower bounds for Hausdorff dimension, and applies these results to sum-product problems and projection questions.
Contribution
It fully resolves the Furstenberg set conjecture in , providing exact dimension bounds and connecting to sum-product estimates and projection problems.
Findings
Furstenberg sets in have Hausdorff dimension at least min(s+t, (3s+t)/2, s+1)
Derived an Elekes-type bound for discretized sum-product problem
Resolved an orthogonal projection question of Oberlin
Abstract
We fully resolve the Furstenberg set conjecture in , that a -Furstenberg set has Hausdorff dimension . As a result, we obtain an analogue of Elekes' bound for the discretized sum-product problem and resolve an orthogonal projection question of Oberlin.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Point processes and geometric inequalities · Mathematical Approximation and Integration
