An improved bound on the Hausdorff dimension of Besicovitch sets in ${\mathbb{R}}^3$

Nets Hawk Katz, Joshua Zahl

We prove that any Besicovitch set in ${\mathbb{R}}^3$ must have Hausdorff dimension at least $5/2+{\epsilon }_0$ for some small constant ${\epsilon }_0>0$. This follows from a more general result about…