A restriction estimate for surfaces with negative Gaussian curvatures

TL;DR

This paper establishes $L^p$ bounds for Fourier extension operators on surfaces with negative Gaussian curvature in three-dimensional space, advancing understanding in harmonic analysis.

Contribution

It provides new $L^p$ restriction estimates for negatively curved surfaces, extending previous results to a broader class of surfaces.

Findings

Proves $L^p$ bounds for $p>3.25$ on surfaces with negative Gaussian curvature

Extends restriction theory to negatively curved surfaces in $\

Advances harmonic analysis techniques for non-positively curved surfaces.

Abstract

We prove $L^p$ bounds for the Fourier extension operators associated to surfaces in $\mathbb{R}^3$ with negative Gaussian curvatures for every $p>3.25$.