2022/05/16 by Ben Lund, Lund, Ben, Thang V. Pham +3 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2205.07431
openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen (2016), Orponen (2018), and Liu (2020) to finite spaces. In some cases, our results are stronger than the corresponding results in the continuous setting. In particular, we solve the finite field analog of a conjecture due to Liu and Orponen on the exceptional set of radial projections of a set of dimension between d-2 and d-1.