Decouplings for curves and hypersurfaces with nonzero Gaussian curvature

Abstract

We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from \cite{BD3}. As a consequence of this we obtain sharp (up to $ε$ losses) Strichartz estimates for the hyperbolic Schrödinger equation on the torus. Our second main result is an $l^2$ decoupling for non degenerate curves which has implications for Vinogradov's mean value theorem.

This article subsumes the results of arXiv:1407.0291. Final version, incorporating referee's suggestions