The multilinear restriction estimate: almost optimality and localization

TL;DR

This paper advances the understanding of multilinear restriction estimates by developing an epsilon-removal technique and refining estimates under localization conditions, enhancing their applicability and precision.

Contribution

It introduces a general epsilon-removal argument and refines multilinear restriction estimates for localized terms, generalizing previous results.

Findings

Epsilon-removal argument for multilinear restriction estimate

Refined estimates for localized terms

Generalization of prior multilinear restriction results

Abstract

The first result in this paper provides a very general $\epsilon$-removal argument for the multilinear restriction estimate. The second result provides a refinement of the multilinear restriction estimate in the case when some terms have appropriate localization properties; this generalizes a prior result of the author.