Some structure of Kakeya sets in R^3.
Some structure of Kakeya sets in R^3.

Hong Wang, Courant Institute
Fine Hall 314
A Kakeya set in R^n is a set of points that contains a unit line segment in every direction. We study the structure of Kakeya sets in R^3 and show that for any Kakeya set K, there exists wellseparated scales 0<\delta<\rho\leq 1 so that the \deltaneighborhood of K is almost as large as the \rhoneighborhood of K. As a consequence, every Kakeya set in R^3 has Assouad dimension 3. This is joint work with Josh Zahl.