A Continuum Beck-type Theorem for Hyperplanes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915549021208576 |
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| author | Bright, Paige Ortiz, Alexander Zakharov, Dmitrii |
| author_facet | Bright, Paige Ortiz, Alexander Zakharov, Dmitrii |
| contents | We prove a sharp continuum Beck-type theorem for hyperplanes. Our work is inspired by foundational work of Beck on the discrete problem, as well as refinements due to Do and Lund. The inductive proof uses recent breakthrough results in projection theory by Orponen--Shmerkin--Wang and Ren, who proved continuum Beck-type theorems for lines in $\mathbb{R}^2$ and $\mathbb{R}^n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Continuum Beck-type Theorem for Hyperplanes Bright, Paige Ortiz, Alexander Zakharov, Dmitrii Classical Analysis and ODEs Combinatorics 28A75, 28A78 We prove a sharp continuum Beck-type theorem for hyperplanes. Our work is inspired by foundational work of Beck on the discrete problem, as well as refinements due to Do and Lund. The inductive proof uses recent breakthrough results in projection theory by Orponen--Shmerkin--Wang and Ren, who proved continuum Beck-type theorems for lines in $\mathbb{R}^2$ and $\mathbb{R}^n$. |
| title | A Continuum Beck-type Theorem for Hyperplanes |
| topic | Classical Analysis and ODEs Combinatorics 28A75, 28A78 |
| url | https://arxiv.org/abs/2510.10907 |