New bound on the Hausdorff dimension of Kakeya sets in ${\mathbb{R}}^4$

Abstract

We obtain a slight improvement to the trilinear bound of Guth-Zahl by application of Wang-Zahl's resolution of 3-D Kakeya to tubes inside a thickened neighborhood of a variety. This is combined with the planebrush argument of Katz and Zahl to obtain the new bound of 3.073.