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 [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 l 2 decoupling for nondegenerate curves, which has implications for Vinogradov’s mean value theorem.
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The first author is partially supported by the NSF grant DMS-1301619.
The second author is partially supported by the NSF Grant DMS-1161752.
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Bourgain, J., Demeter, C. Decouplings for curves and hypersurfaces with nonzero Gaussian curvature. JAMA 133, 279–311 (2017). https://doi.org/10.1007/s11854-017-0034-3
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DOI: https://doi.org/10.1007/s11854-017-0034-3