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Incidence bounds related to circular Furstenberg sets

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arxiv 2502.10686 v1 pith:OPGR6KIJ submitted 2025-02-15 math.CA math.APmath.CO

John Green , Terence L. J. Harris , Yumeng Ou , Kevin Ren , Sarah Tammen This is my paper · ORCID
classification math.CAmath.APmath.CO
keywords boundscircularfamiliesfurstenbergprovesetsapproximatebound
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abstract

We prove bounds on approximate incidences between families of circles and families of points in the plane. As a consequence, we prove a lower bound for the dimension of circular $(u,v)$-Furstenberg sets, which is new for large $u$ and $v$.

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  1. Furstenberg set theorem for transversal families of functions

    math.CA 2025-08 conditional novelty 7.0 of 10

    A sharp dimension bound for Furstenberg sets built from transversal families of graphs, with an application to Fourier decay of fractal measures on convex curves.

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