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 $\epsilon$ 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2014
 arXiv:
 arXiv:1409.1634
 Bibcode:
 2014arXiv1409.1634B
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Analysis of PDEs;
 Mathematics  Number Theory
 EPrint:
 This article subsumes the results of arXiv:1407.0291. Final version, incorporating referee's suggestions