2022
DOI: 10.48550/arxiv.2205.13890
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On exceptional sets of radial projections

Abstract: We prove two new exceptional set estimates for radial projections in the plane.The finite field counterparts of both results above were recently proven by Lund, Thang, and Huong Thu. Our results resolve the planar cases of conjectures of Lund-Thang-Huong Thu, and Liu. CONTENTS1. Introduction 1 1.1. Sharper results for sets avoiding lines? 3 1.2. Paper outline 4 1.3. Notation 4 Acknowledgements 4 2. Reduction to a δ-discretised problem 4 2.1. Proof of Proposition 2.3 6 3. Proof of Theorem 2.5 12 4. Proof of The… Show more

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“…where the last inequality is by the s-dimensional condition of T V . Plugging this back into (12), we obtain…”
Section: Discretized Falconer-type Estimatementioning
confidence: 99%
See 4 more Smart Citations
“…where the last inequality is by the s-dimensional condition of T V . Plugging this back into (12), we obtain…”
Section: Discretized Falconer-type Estimatementioning
confidence: 99%
“…Recently, Orponen and Shmerkin [12] proved the n = 2 case for both Theorem 1 and Theorem 2. Their proof of Theorem 1 (when n = 2) is based on a Furstenbergtype estimate due to Fu and Ren [3].…”
Section: Introductionmentioning
confidence: 97%
See 3 more Smart Citations