An improved bound for the dimension of $(α,2α)$-Furstenberg sets
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866910566908428288 |
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| author | Héra, Kornélia Shmerkin, Pablo Yavicoli, Alexia |
| author_facet | Héra, Kornélia Shmerkin, Pablo Yavicoli, Alexia |
| contents | We show that given $α\in (0, 1)$ there is a constant $c=c(α) > 0$ such that any planar $(α, 2α)$-Furstenberg set has Hausdorff dimension at least $2α+ c$. This improves several previous bounds, in particular extending a result of Katz-Tao and Bourgain. We follow the Katz-Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_11304 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | An improved bound for the dimension of $(α,2α)$-Furstenberg sets Héra, Kornélia Shmerkin, Pablo Yavicoli, Alexia Classical Analysis and ODEs Combinatorics Metric Geometry Primary: 28A78, 05B30 We show that given $α\in (0, 1)$ there is a constant $c=c(α) > 0$ such that any planar $(α, 2α)$-Furstenberg set has Hausdorff dimension at least $2α+ c$. This improves several previous bounds, in particular extending a result of Katz-Tao and Bourgain. We follow the Katz-Tao approach with suitable changes, along the way clarifying, simplifying and/or quantifying many of the steps. |
| title | An improved bound for the dimension of $(α,2α)$-Furstenberg sets |
| topic | Classical Analysis and ODEs Combinatorics Metric Geometry Primary: 28A78, 05B30 |
| url | https://arxiv.org/abs/2001.11304 |