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On the projections of almost Ahlfors regular sets

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arxiv 2411.04528 v1 pith:FJLKMRD4 submitted 2024-11-07 math.CA

Tuomas Orponen , Kevin Ren This is my paper · ORCID
classification math.CA
keywords ahlforsregularsetsclassprojectionsharptheoremalmost
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abstract

We show that the "sharp Kaufman projection theorem" from 2023 is sharp in the class of Ahlfors $(1,\delta^{-\epsilon})$-regular sets. This is in contrast with a recent result of the first author, which improves the projection theorem in the class of Ahlfors $(1,C)$-regular sets.

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  1. Universal Sets for Projections

    math.CA 2024-11 conditional novelty 7.0 of 10

    There exist direction sets of Hausdorff dimension zero that are universal for AD-regular planar sets, and direction sets of arbitrarily small positive dimension universal for weakly regular sets.

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