2021/12/15 by Daniel Di Benedetto, Joshua Zahl, Di Benedetto, Daniel +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2112.08249
openalex publication_date 2021/12/15 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We use recent advances on the discretized sum-product problem to obtain new bounds on the Hausdorff dimension of planar (α,2α)-Fursterberg sets. This provides a quantitative improvement to the 2α+ε bound of Héra-Shmerkin-Yavicoli. In particular, we show that every 1/2-Furstenberg set has dimension at least 1 + 1/4536.