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arXiv · 2408.04885

Exceptional sets for length under restricted families of projections onto lines in $\mathbb{R}^3$

Terence L. J. Harris
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Abstract

It is shown that if $A \subseteq \mathbb{R}^3$ is a Borel set of Hausdorff dimension $\dim A>1$, and if $ρ_θ$ is orthogonal projection to the line spanned by $( \cos θ, \sin θ, 1 )$, then $ρ_θ(A)$ has positive length for all $θ$ outside a set of Hausdorff dimension at most $\frac{3-\dim A}{2}$.

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Terence L. J. Harris. 2024-10-12. Exceptional sets for length under restricted families of projections onto lines in $\mathbb{R}^3$. https://arxiv.org/abs/2408.04885

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