The trilinear restriction estimate with sharp dependence on the transversality

TL;DR

This paper enhances the trilinear restriction estimate for paraboloid subsets in three dimensions by establishing a sharp dependence on transversality, advancing understanding in harmonic analysis.

Contribution

It provides the first sharp transversality-dependent bound for the Bennett--Carbery--Tao trilinear restriction estimate in three dimensions.

Findings

Established the sharp transversality dependence in the restriction estimate.

Improved the bound for subsets of the paraboloid in three dimensions.

Contributed to the theory of harmonic analysis with precise estimates.

Abstract

We improve the Bennett--Carbery--Tao trilinear restriction estimate for subsets of the paraboloid in three dimensions, giving the sharp factor depending on the transversality.