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Discretized Radial Projections in $\mathbb{R}^d$ (2309.04097v1)
Published 8 Sep 2023 in math.CA, math.CO, and math.MG
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 $\mathbb{R}d$.