On the dimension of visible parts

2019/12/23 by Tuomas Orponen, Orponen, Tuomas
Engineering · Mathematics · #28A78 (secondary) #28A80 (primary) #Advanced Numerical Analysis Techniques #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1912.10898

openalex publication_date 2019/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I prove that the visible parts of a compact set in ℝⁿ, n ≥ 2, have Hausdorff dimension at most n - \tfrac150n from almost every direction.

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