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

• Kornélia Héra ^[1] ; Pablo Shmerkin ^[2] ; Alexia Yavicoli ^[3]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
  2. [2] Universidad Torcuato Di Tella

     Universidad Torcuato Di Tella

     Argentina

     
  3. [3] University of British Columbia

     University of British Columbia

     Canadá

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 1, 2022, págs. 295-322
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.