A note on the restriction theorem and geometry of hypersurfaces - Nicola, Fabio (MATHEMATICA SCANDINAVICA, 2008)
A necessary condition is established for the optimal (L^p,L^2) restriction theorem to hold on a hypersurface S, in terms of its Gaussian curvature. For some classes of flat hypersurface we give sharp thresholds for the range of admissible exponents p, depending on the specific geometry.