10 papers
A streamlined proof of the Kakeya set conjecture in
Larry Guth, Hong Wang, Joshua Zahl
We present a streamlined and simplified proof of the Kakeya set conjecture in .
On the number of pairwise touching cylinders in
Jozsef Solymosi, Josh Zahl
John E. Littlewood posted the question {\em ``Is it possible in 3-space for seven infinite circular cylinders of unit radius each to touch all the others? Seven is the number sugge…
A Survey of the Kakeya conjecture, 2000-2025
Joshua Zahl
We survey progress on the Kakeya conjecture in Euclidean space, with an emphasis on developments that have occurred since the previous surveys by Wolff and Katz-Tao.
On Maximal Functions Associated to Families of Curves in the Plane
Joshua Zahl
We consider the mapping properties of maximal averages associated to families of curves, and thickened curves, in the plane. These include the (planar) Kakeya maximal functio…
Sticky Kakeya sets and the sticky Kakeya conjecture
Hong Wang, Joshua Zahl
A Kakeya set is a compact subset of that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that such sets must have Hausdorff a…
A Kakeya maximal function estimate in four dimensions using planebrushes
Nets Hawk Katz, Joshua Zahl
We obtain an improved Kakeya maximal function estimate and improved Kakeya Hausdorff dimension estimate in using a new geometric argument called the planebrush. A pl…