Hausdorff dimension of Besicovitch sets of Cantor graphs

Abstract: It is well known that planar Besicovitch sets – sets containing a unit line segment in every direction – have Hausdorff dimension 2. In a joint work with Iqra Altaf and Marianna Csörnyei we consider Besicovitch sets of Cantor graphs in the plane– sets containing a rotated (and translated) copy of a fixed Cantor graph (its line segments of course removed) in every direction, and prove lower bounds for their Hausdorff dimension.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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