2 problems

Discretized sticky Kakeya conjecture. For every $\varepsilon>0$ there exist $\eta=\eta_{n,\mathrm{rest}}(\varepsilon)>0$ and $\delta_0=\delta_{0,n,\mathrm{rest}}(\varepsilon)>0$ su…

Sticky curved Kakeya conjecture. If $\phi$ satisfies Bourgain's condition, then sticky $\phi$-Kakeya sets in $\mathbb{R}^n$ have Hausdorff dimension $n$.