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arXiv · 1409.1634

Decouplings for curves and hypersurfaces with nonzero Gaussian curvature

Jean Bourgain·Ciprian Demeter
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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 Schr\"odinger 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.

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Jean Bourgain, Ciprian Demeter. 2014-09-05. Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. https://arxiv.org/abs/1409.1634

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