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arXiv · 2208.12687

Hausdorff dimension of Besicovitch sets of Cantor graphs

Iqra Altaf·Marianna Csörnyei·Kornélia Héra
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Abstract

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

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Iqra Altaf, Marianna Csörnyei, Kornélia Héra. 2022-08-26. Hausdorff dimension of Besicovitch sets of Cantor graphs. https://arxiv.org/abs/2208.12687

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