Decouplings for curves and hypersurfaces with nonzero Gaussian curvature

By Jean Bourgain, Ciprian Demeter. 2014

113 citations recorded by the source corpus.

We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from [4]. 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 l2 decoupling for nondegenerate curves, which has implications for Vinogradov’s mean value theorem.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d34f0a1ff890399301fc8780f2fc7c40b456a679

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the Vinogradov mean value (2016, background): “t out that there is a similar decoupling inequality for 2 ≤ p<k(k+ 1), though for k≥ 3 this is not just a consequence of interpolation. (iii) Our decoupling inequalities for curves appear in [B1], [BD2], [B2]. In particular, the reader is referred to [B2] for an application to exponential sums an”
Sharp estimates for oscillatory integral operators via polynomial partitioning (2017, background): “(33) It is remarked that non-trivial `p-decoupling estimates are known to hold for the full hyperbolic paraboloid; see [8].”
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, methodology): “In the earlier work [7], only the weakest result in this hierarchy was used (a variant of the k = 1 case from Theorem 6.5).”