Incidence estimates for quasi-product sets and applications
Classical Analysis and ODEs
2025-11-21 v1 Combinatorics
Abstract
We use recent advances in the theory of Furstenberg sets to prove new incidence results of Szemer\'edi--Trotter strength for -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.
Cite
@article{arxiv.2511.15899,
title = {Incidence estimates for quasi-product sets and applications},
author = {Ciprian Demeter and William O'Regan},
journal= {arXiv preprint arXiv:2511.15899},
year = {2025}
}
Comments
Setup/notation in subsection 4.3 overlaps with that in arXiv:2406.06884v1