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arXiv · 2204.01770

Dimension Estimates on Circular $(s,t)$-Furstenberg Sets

Jiayin Liu
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Abstract

In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimension at least $$\max\{\frac{t}3+s,(2t+1)s-t\} \text{ for all $0<s,t\le 1$}.$$ This result extends the previous dimension estimates on circular Kakeya sets by Wolff.

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Jiayin Liu. 2022-04-04. Dimension Estimates on Circular $(s,t)$-Furstenberg Sets. https://arxiv.org/abs/2204.01770

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