A Uniform Estimate for Fourier Restriction to Simple Curves

TL;DR

This paper establishes a uniform estimate for the Fourier restriction problem applied to a specific class of simple curves in multi-dimensional Euclidean space, advancing understanding of Fourier analysis on curved manifolds.

Contribution

It provides a new uniform Fourier extension-restriction estimate for simple curves, which was previously unknown or less understood.

Findings

Proved a uniform Fourier restriction estimate for simple curves

Extended Fourier analysis techniques to a broader class of curves

Improved bounds for Fourier extension operators on simple curves

Abstract

We prove a uniform Fourier extension-restriction estimate for a certain class of curves in d-dimensional Euclidean space.