An exceptional set estimate for restricted projections to lines in ℝ³

2022/09/30 by Shengwen Gan, Larry Guth, Gan, Shengwen +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2209.15152

openalex publication_date 2022/09/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Let γ:[0,1]→ \mathbbS² be a non-degenerate curve in ℝ³, that is to say, det(γ(θ),γ'(θ),γ''(θ))≠ 0. For each θ∈[0,1], let l_θ=\tγ(θ):t∈ℝ\ and ρ_θ:ℝ³→ l_θ be the orthogonal projections. We prove an exceptional set estimate. For any Borel set A⊂ℝ³ and 0≤ s≤ 1, define E_s(A):=\θ∈[0,1]: dim(ρ_θ(A))

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