Kakeya and Furstenberg problems for sticky sets of tubes

We study incidence problems for sticky sets of tubes. In the first part, we prove a sharp Furstenberg set estimate for sticky sets of tubes in ${\mathbb{R}}^3$ satisfying convex Wolff axioms. In the second part, we prove the Kakeya set conjecture in ${\mathbb{R}}^4$ for sticky sets of tubes satisfying convex Wolff axioms.