An improved restriction estimate in $\mathbb{R}^3$

TL;DR

This paper advances the understanding of Fourier restriction estimates in three-dimensional space by improving the range of p for which the estimate holds, utilizing Kakeya incidence estimates and refined decoupling techniques.

Contribution

It provides a new restriction estimate in -dimensional space, extending the known range of p through novel incidence and decoupling methods.

Findings

Improved restriction estimate for p>3+3/14 in D

Utilized Kakeya type incidence estimates

Applied refined decoupling theorem

Abstract

We improve the $L^{p}\rightarrow L^p$ restriction estimate in $\mathbb{R}^3$ to the range $p>3+3/14$, based on some Kakeya type incidence estimates and the refined decoupling theorem.