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arXiv · 2207.02259

A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb{R}^3$

Malabika Pramanik·Tongou Yang·Joshua Zahl
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Abstract

We resolve a conjecture of F\"assler and Orponen on the dimension of exceptional projections to one-dimensional subspaces indexed by a space curve in $\mathbb{R}^3$. We do this by obtaining sharp $L^p$ bounds for a variant of the Wolff circular maximal function over fractal sets for a class of $C^2$ curves related to Sogge's cinematic curvature condition. A key new tool is the use of lens cutting techniques from discrete geometry.

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Malabika Pramanik, Tongou Yang, Joshua Zahl. 2022-07-05. A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb{R}^3$. https://arxiv.org/abs/2207.02259

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