Geodesic
On the Hausdorff dimension of circular Furstenberg sets
Discrete analysis (2024) Cet article a éte moissonné depuis la source Scholastica

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For $0 \leq s \leq 1$ and $0 \leq t \leq 3$, a set $F \subset \mathbb{R}^{2}$ is called a circular $(s,t)$-Furstenberg set if there exists a family of circles $\mathcal{S}$ of Hausdorff dimension $\dim_{\mathrm{H}} \mathcal{S} \geq t$ such that $$\dim_{\mathrm{H}} (F \cap S) \geq s, \qquad S \in \mathcal{S}.$$ We prove that if $0 \leq t \leq s \leq 1$, then every circular $(s,t)$-Furstenberg set $F \subset \mathbb{R}^{2}$ has Hausdorff dimension $\dim_{\mathrm{H}} F \geq s + t$. The case $s = 1$ follows from earlier work of Wolff on circular Kakeya sets.
Publié le : 
@article{DAS_2024_a3,
     author = {Katrin F\"assler and Jiayin Liu and Tuomas Orponen},
     title = {On the {Hausdorff} dimension of circular {Furstenberg} sets},
     journal = {Discrete analysis},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2024_a3/}
}
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AU  - Katrin Fässler
AU  - Jiayin Liu
AU  - Tuomas Orponen
TI  - On the Hausdorff dimension of circular Furstenberg sets
JO  - Discrete analysis
PY  - 2024
UR  - http://geodesic.mathdoc.fr/item/DAS_2024_a3/
LA  - en
ID  - DAS_2024_a3
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%0 Journal Article
%A Katrin Fässler
%A Jiayin Liu
%A Tuomas Orponen
%T On the Hausdorff dimension of circular Furstenberg sets
%J Discrete analysis
%D 2024
%U http://geodesic.mathdoc.fr/item/DAS_2024_a3/
%G en
%F DAS_2024_a3
Katrin Fässler; Jiayin Liu; Tuomas Orponen. On the Hausdorff dimension of circular Furstenberg sets. Discrete analysis (2024). http://geodesic.mathdoc.fr/item/DAS_2024_a3/