Discretized Radial Projections in ℝ^d

2023/09/08 by Kevin Ren, Ren, Kevin
Mathematics · #28A78 #28A80 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2309.04097

openalex publication_date 2023/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an ε-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 δ-tubes and a quasi-product set of δ-balls in ℝ^d.

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