Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates

Abstract

Recently Wolff obtained a nearly sharp $L^2$ bilinear restriction theorem for bounded subsets of the cone in general dimension. We obtain the endpoint of Wolff's estimate and generalize to the case when one of the subsets is large. As a consequence, we are able to deduce some nearly-sharp $L^p$ null form estimates.

41 pages, no figures, submitted to Math Z. Revision corrects some serious errors in previous version. Several expository comments have also been added