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.
Incidence bounds related to circular Furstenberg sets
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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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Furstenberg set theorem for transversal families of functions
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.