On the restriction theorem for paraboloid in ${\mathbb{R}}^4$

Abstract

We prove that recent breaking by Zahl of the $\frac{3}{2}$ barrier in Wolff's estimate on the Kakeya maximal operator in ${\mathbb{R}}^4$ leads to improving the $\frac{14}{5}$ threshold for the restriction problem for the paraboloid in ${\mathbb{R}}^4$. One of the ingredients is a new trilinear estimate. The proofs are deliberately presented in a nontechnical and concise format, so as to make the arguments more readable and focus attention on the key tools.

The result is unconditional now