# Fourier Restriction to a Hyperbolic Cone

## TL;DR

This paper proves the Fourier restriction conjecture for a hyperbolic cone in four-dimensional space by applying bilinear restriction theorems and bilinear-to-linear techniques.

## Contribution

It establishes the conjectured restriction estimates for a hyperbolic cone in -dimensional space, advancing the understanding of Fourier analysis on such hypersurfaces.

## Key findings

- Confirmed the Fourier restriction conjecture for hyperbolic cones in D.
- Applied bilinear restriction theorems to hyperbolic cross sections.
- Extended bilinear-to-linear methods to this geometric setting.

## Abstract

Using a bilinear restriction theorem of Lee and a bilinear-to-linear argument of Stovall, we obtain the conjectured range of Fourier restriction estimates for a conical hypersurface in $\mathbb{R}^4$ with hyperbolic cross sections.