Fourier restriction estimates for surfaces of co-dimension two in $\mathbb{R}^5$

TL;DR

This paper establishes sharp Fourier restriction estimates for certain 3D quadratic surfaces in five-dimensional space, advancing understanding of harmonic analysis on these geometric objects.

Contribution

It provides the first sharp $L^p ightarrow L^q$ restriction estimates for specific classes of 3D quadratic surfaces in $R^5$, up to endpoint cases.

Findings

Sharp restriction estimates proved for some classes of surfaces.

Results are optimal up to endpoint cases.

Advances the theory of Fourier analysis on quadratic surfaces.

Abstract

We prove $L^p \rightarrow L^q$ Fourier restriction estimates for 3-dimensional quadratic surfaces in $\mathbb{R}^5$. Our results are sharp, up to endpoints, for a few classes of surfaces.