Fourier restriction to smooth enough curves

TL;DR

This paper establishes Fourier restriction estimates for smooth compact curves in higher dimensions without nondegeneracy assumptions, extending the range of applicability using affine arclength measures.

Contribution

It proves restriction estimates for arbitrary smooth curves in the Drury range without requiring nondegeneracy, utilizing affine arclength measures as a key tool.

Findings

Restriction estimates hold for all smooth curves with N > d

No nondegeneracy condition needed on the curves

Uses affine arclength measure to achieve sharp results

Abstract

We prove Fourier restriction estimates to arbitrary compact $C^{N}$ curves for any $N > d$ in the (sharp) Drury range, using a power of the affine arclength measure as a mitigating factor. In particular, we make no nondegeneracy assumption on the curve.