Global restriction estimates for elliptic hyperboloids

TL;DR

This paper establishes global Fourier restriction estimates for elliptic hyperboloids across dimensions, advancing understanding in harmonic analysis and extending previous joint work.

Contribution

It provides unconditional restriction estimates in the bilinear range and extends results conditionally towards the local restriction conjecture for elliptic surfaces.

Findings

Proves global restriction estimates for elliptic hyperboloids in all dimensions d ≥ 2.

Extends previous results with Oliveira e Silva and Stovall.

Achieves unconditional results in the bilinear range q > 2(d+3)/(d+1).

Abstract

We prove global Fourier restriction estimates for elliptic, or two-sheeted, hyperboloids of arbitrary dimension $d \geq 2$, extending recent joint work with Oliveira e Silva and Stovall. Our results are unconditional in the (adjoint) bilinear range, $q > \frac{2(d+3)}{d+1}$, and extend conditionally upon further progress toward the local restriction conjecture for elliptic surfaces.