# A cone restriction estimate using polynomial partitioning

### Yumeng Ou

University of Pennsylvania, Philadelphia, USA### Hong Wang

UCLA, Los Angeles, USA

## Abstract

We obtain an improved Fourier restriction estimate for a truncated cone using the method of polynomial partitioning in dimension $n\geq 3$, which in particular solves the cone restriction conjecture for $n=5$, and recovers the sharp range for $3\leq n\leq 4$. The main ingredient of the proof is a $k$-broad estimate for the cone extension operator, which is a weak version of the $k$-linear cone restriction conjecture for $2\leq k\leq n$.

## Cite this article

Yumeng Ou, Hong Wang, A cone restriction estimate using polynomial partitioning. J. Eur. Math. Soc. 24 (2022), no. 10, pp. 3557–3595

DOI 10.4171/JEMS/1168