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

Volume 156 / 2019

Ciprian Demeter Colloquium Mathematicum 156 (2019), 301-311 MSC: Primary 42B15; Secondary 42B20. DOI: 10.4064/cm7393-9-2018 Published online: 14 February 2019


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.


  • Ciprian DemeterDepartment of Mathematics
    Indiana University
    Bloomington, IN 47405, U.S.A.

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