Incidence estimates for quasi-product sets and applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911276830031872 |
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| author | Demeter, Ciprian O'Regan, William |
| author_facet | Demeter, Ciprian O'Regan, William |
| contents | We use recent advances in the theory of Furstenberg sets to prove new incidence results of Szemerédi--Trotter strength for $δ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incidence estimates for quasi-product sets and applications Demeter, Ciprian O'Regan, William Classical Analysis and ODEs Combinatorics We use recent advances in the theory of Furstenberg sets to prove new incidence results of Szemerédi--Trotter strength for $δ$-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. |
| title | Incidence estimates for quasi-product sets and applications |
| topic | Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2511.15899 |