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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.15760 |
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| _version_ | 1866915206333988864 |
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| author | Nadjimzadah, Arian |
| author_facet | Nadjimzadah, Arian |
| contents | We give new lower bounds for the Hausdorff dimension of Kakeya sets built from various families of curves in $\mathbb R^3$, going beyond what the polynomial partitioning method has so-far achieved. We do this by combining Wolff's classical hairbrush argument with a new incidence bound for 3-parameter families of curves which satisfy conditions we call coniness and twistiness. Our main argument builds off a technique of Katz, Wu, and Zahl used in the study of $\rm{SL}_2$-Kakeya sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New curved Kakeya estimates Nadjimzadah, Arian Classical Analysis and ODEs We give new lower bounds for the Hausdorff dimension of Kakeya sets built from various families of curves in $\mathbb R^3$, going beyond what the polynomial partitioning method has so-far achieved. We do this by combining Wolff's classical hairbrush argument with a new incidence bound for 3-parameter families of curves which satisfy conditions we call coniness and twistiness. Our main argument builds off a technique of Katz, Wu, and Zahl used in the study of $\rm{SL}_2$-Kakeya sets. |
| title | New curved Kakeya estimates |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.15760 |