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arXiv · 2511.15899

Incidence estimates for quasi-product sets and applications

Ciprian Demeter·William O'Regan
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Abstract

We use recent advances in the theory of Furstenberg sets to prove new incidence results of Szemer\'edi--Trotter strength for $\delta$-discretized structures with Cartesian product flavor. We use these results to make progress on a number of problems that include energy estimates and Fourier decay of fractal measures supported on curves, as well as various sum-product-like results governed by fractal dimension.

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Ciprian Demeter, William O'Regan. 2025-11-19. Incidence estimates for quasi-product sets and applications. https://arxiv.org/abs/2511.15899

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