A bound for plany Kakeya sets in $\mathbb{F}_q^4$ using the planebrush method
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917193434791936 |
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| author | Łaba, Izabella Choudhuri, Mukul Rai Zahl, Joshua |
| author_facet | Łaba, Izabella Choudhuri, Mukul Rai Zahl, Joshua |
| contents | Katz and Zahl used a planebrush argument to prove that Kakeya sets in $\mathbb{R}^4$ have Hausdorff dimension at least 3.059. In the special case when the Kakeya set is plany, their argument gives a better lower bound of 10/3. We give a nontechnical exposition of the Katz-Zahl argument for plany Kakeya sets in the finite field setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A bound for plany Kakeya sets in $\mathbb{F}_q^4$ using the planebrush method Łaba, Izabella Choudhuri, Mukul Rai Zahl, Joshua Classical Analysis and ODEs Combinatorics Katz and Zahl used a planebrush argument to prove that Kakeya sets in $\mathbb{R}^4$ have Hausdorff dimension at least 3.059. In the special case when the Kakeya set is plany, their argument gives a better lower bound of 10/3. We give a nontechnical exposition of the Katz-Zahl argument for plany Kakeya sets in the finite field setting. |
| title | A bound for plany Kakeya sets in $\mathbb{F}_q^4$ using the planebrush method |
| topic | Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2507.09605 |