Favard length and quantitative rectifiability

2024/08/07 by Damian Dąbrowski, Dąbrowski, Damian · 1 citation
Computer Science · #28A75 (primary) 28A78 (secondary) #Classical Analysis and ODEs (math.CA) #Computability, Logic, AI Algorithms #FOS: Mathematics #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2408.03919

openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Favard length of a Borel set E⊂ℝ² is the average length of its orthogonal projections. We prove that if E is Ahlfors 1-regular and it has large Favard length, then it contains a big piece of a Lipschitz graph. This gives a quantitative version of the Besicovitch projection theorem. As a corollary, we answer questions of David and Semmes and of Peres and Solomyak. We also make progress on Vitushkin's conjecture.

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• Sharp Favard length of random Cantor sets

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