The optimal trilinear restriction estimate for a class of hypersurfaces with curvature

Abstract

Bennett, Carbery and Tao established nearly optimal $L^1$ trilinear restriction estimates in ${\mathbb{R}}^{n+1}$ under transversality assumptions only. In this paper we show that the curvature improves the range of exponents, by establishing $L^p$ estimates, for any $p>\frac{2(n+4)}{3(n+2)}$ in the case of double-conic surfaces. The exponent $\frac{2(n+4)}{3(n+2)}$ is shown to be the universal threshold for the trilinear estimate.

arXiv commentarXiv admin note: text overlap with arXiv:1601.01000