On Cone Restriction Estimates in Higher Dimensions

TL;DR

This paper improves bounds for cone restriction estimates in higher dimensions by refining polynomial partitioning techniques and recursive algorithms, building on Ou-Wang's approach.

Contribution

It introduces a recursive algorithm framework that incorporates nested polynomial Wolff axioms to enhance cone restriction bounds in higher dimensions.

Findings

Achieved improved bounds for cone restriction estimates.

Recasted Ou-Wang's approach as a recursive algorithm.

Integrated nested polynomial Wolff axioms into the analysis.

Abstract

We revisit the Ou-Wang's approach to the cone restriction problem via polynomial partitioning. By recasting their inductive scheme as a recursive algorithm and incorporating the nested polynomial Wolff axioms, we obtain improved bounds for cone restriction estimates in higher dimensions.