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

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arxiv 2309.04097 v1 pith:3OLVQDLH submitted 2023-09-08 math.CA math.COmath.MG

Kevin Ren This is my paper · ORCID
classification math.CAmath.COmath.MG
keywords deltadiscretizedmathbbprojectionradialtheoremballsdimensions
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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 $\mathbb{R}^d$.

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Cited by 1 Pith paper

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  1. Pinned Dot Product Set Estimates

    math.CA 2024-12 conditional novelty 7.0 of 10

    Pinned dot product sets are large when the underlying set has Hausdorff dimension above n/2 with spread translations, or above (n+1)/2 for any translation, proven by reducing dot products to orthogonal projections.

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