English

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

Classical Analysis and ODEs 2018-01-17 v3

Abstract

We prove that recent breaking by Zahl of the 32\frac32 barrier in Wolff's estimate on the Kakeya maximal operator in R4\mathbb R^4 leads to improving the 145\frac{14}{5} threshold for the restriction problem for the paraboloid in R4\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.

Cite

@article{arxiv.1701.03523,
  title  = {On the restriction theorem for paraboloid in $\mathbb R^4$},
  author = {Ciprian Demeter},
  journal= {arXiv preprint arXiv:1701.03523},
  year   = {2018}
}

Comments

The result is unconditional now

R2 v1 2026-06-22T17:49:11.035Z