Hausdorff dimension of Besicovitch sets of Cantor graphs

2022/08/26 by Iqra Altaf, Altaf, Iqra, Marianna Csörnyei +3
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2208.12687

openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets Γ, i.e. sets that contain a rotated copy of Γ in each direction. We show that for a large class of Cantor sets C and Cantor-graphs Γ built on C, the Hausdorff dimension of any Γ-Besicovitch set must be at least min(2-s²,(1)/(s)), where s=dim C.

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