Resumen de Restriction and decay for flat hypersurfaces

Anthony Carbery , Sarah Ziesler

• In the first part we consider restriction theorems for hypersurfaces $\Gamma$ in ${\mathbf R}^n$, with the affine curvature $K_{\Gamma}^{1/(n+1)}$ introduced as a mitigating factor. Sjölin, [19], showed that there is a universal restriction theorem for all convex curves in ${\mathbf R}^2$. We show that in dimensions greater than two there is no analogous universal restriction theorem for hypersurfaces with non-negative curvature.