Resumen de An improved bound for the dimension of (α,2α)-Furstenberg sets

Kornélia Héra, Pablo Shmerkin, Alexia Yavicoli

• We show that given α∈(0,1) there is a constant c=c(α)>0 such that any planar (α,2α)-Furstenberg set has Hausdorff dimension at least 2α+c. This improves several previous bounds, in particular extending a result of Katz–Tao and Bourgain. We follow the Katz–Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps.