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

Abstract We consider a surface with negative curvature in $${{\mathbb {R}}}^3,$$ R 3 , which is cubic perturbation of the saddle. For this surface, we prove new restriction theorem, analogous to theorem for paraboloids proved by L. Guth 2016. This specific has turned out be fundamental importance also understanding more general classes one-variate perturbations, and hope that present paper will further help pave way study perturbations saddle means polynomial partitioning method.