Decouplings for curves and hypersurfaces with nonzero Gaussian curvature

  title={Decouplings for curves and hypersurfaces with nonzero Gaussian curvature},
  author={Jean Bourgain and Ciprian Demeter},
  journal={Journal d'Analyse Math{\'e}matique},
  • Jean Bourgain, Ciprian Demeter
  • Published 2014
  • Mathematics
  • 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. 

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