Sets with Arbitrarily Slow Favard Length Decay

Bobby Wilson

Sets with Arbitrarily Slow Favard Length Decay

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arxiv 1707.08137 v1 pith:BYKWJWHW submitted 2017-07-25 math.CA

Bobby Wilson This is my paper · ORCID

classification math.CA

keywords favardlengthsetsarbitrarilydecayvarepsilonarticlecantor

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abstract

In this article, we consider the concept of the decay of the Favard length of $\varepsilon$-neighborhoods of purely unrectifiable sets. We construct non-self-similar Cantor sets for which the Favard length decays arbitrarily with respect to $\varepsilon$.

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Power Laws for the Favard Length Problem in $\mathbb{R}^d$
math.CA 2025-09 conditional novelty 7.0 of 10

For rational product Cantor sets in R^d (d≥2) with cyclotomic conditions on digit sets, the Favard length of N^{-1}-neighborhoods decays as N^{-ε}, new for d≥3 and for fibered digit sets.

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