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arXiv · 2408.03919

Favard length and quantitative rectifiability

Damian Dąbrowski
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Abstract

The Favard length of a Borel set $E\subset\mathbb{R}^2$ 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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Damian Dąbrowski. 2024-08-07. Favard length and quantitative rectifiability. https://arxiv.org/abs/2408.03919

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