2024/06/14 by Paige Bright, Bright, Paige, Yuqiu Fu +3
Engineering · Mathematics · #28A78 #28A80 #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2406.09707
openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given X,Y⊂ ℝn Borel sets and X≠ ∅. If dim Y ∈ (k,k+1] for some k∈ \1,…, n-1\, then supx∈ X dim πx(Y∖ \x\) ≥ min \dim X + dim Y - k, k\. Our results give a new approach to solving a conjecture of Lund-Pham-Thu in all dimensions and for all ranges of dim Y. The first of our two methods for proving the above theorem is shorter, utilizing a result of the first author and Gan. Our second method, though longer, follows the original methodology of Orponen--Shmerkin--Wang, and requires a higher dimensional incidence estimate and a dual Furstenberg-set estimate for lines. These new estimates may be of independent interest.