Some structure of Kakeya sets in R^3 | Department of Mathematics

Analysis Seminar

Thursday, February 15, 2024 - 3:30pm

Hong Wang

NYU-Courant

Location

University of Pennsylvania

DRL 4E19

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 well-separated scales 0<\delta<\rho\leq 1 so that the \delta-neighborhood of K is almost as large as the \rho-neighborhood of K. As a consequence, every Kakeya set in R^3 has Assouad dimension 3. This is joint work with Josh Zahl.

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