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

Abstract

We prove that the recent breaking (Zahl, 2018) of the 3/2 barrier in Wolff’s estimate on the Kakeya maximal operator in ${\mathbb R}^4$ leads to improving the 14/5 threshold for the restriction problem for the paraboloid in ${\mathbb R}^4$. One of the ingredients is a slight refinement of a certain trilinear estimate (Guth, 2016). The proofs are deliberately presented in a non-technical and concise format, so as to make the arguments more readable and focus attention on the key tools.