Discretized Radial Projections in $\mathbb{R}^d$

TL;DR

This paper extends projection theorems to higher dimensions using new incidence estimates, improving bounds and establishing a discretized radial projection theorem in $\

Contribution

It introduces a generalized Furstenberg-type result and a new incidence estimate for $\

Findings

Improves Kaufman's projection theorem with an $\

Establishes an unconditional discretized radial projection theorem in higher dimensions

Provides a new incidence estimate for $\\delta$-tubes and quasi-product sets in $\

Abstract

We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an $\epsilon$-improvement in Kaufman's projection theorem for hyperplanes and an unconditional discretized radial projection theorem in the spirit of Orponen-Shmerkin-Wang. Our proof relies on a new incidence estimate for $\delta$-tubes and a quasi-product set of $\delta$-balls in $\mathbb{R}^d$.