A Fourier restriction theorem for a perturbed hyperbolic paraboloid: polynomial partitioning

Abstract

We consider a surface with negative curvature in ${\mathbb{R}}^3$ which is a cubic perturbation of the saddle. For this surface, we prove a new restriction theorem, analogous to the theorem for paraboloids proved by L. Guth in 2016. This specific perturbation has turned out to be of fundamental importance also to the understanding of more general classes of perturbations.

26 pages, 1 figure