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

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arxiv 2207.02259 v3 pith:GODDWD7T submitted 2022-07-05 math.CA math.MG

Malabika Pramanik , Tongou Yang , Joshua Zahl This is my paper · ORCID
classification math.CAmath.MG
keywords mathbbasslerboundscinematiccirclescircularclasscondition
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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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  1. A Survey of the Kakeya conjecture, 2000-2025

    math.CA 2025-12 conditional novelty 2.0 of 10

    An authoritative survey of the Kakeya conjecture (2000–2025), organized around the recent proof that Besicovitch sets in R^3 have full Hausdorff and Minkowski dimension 3.

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