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Dimension estimates on circular (s,t)-Furstenberg sets
Jiayin Liusubject
General MathematicsMathematics::Classical Analysis and ODEsMathematics::General TopologyMetric Geometry (math.MG)Hausdorff dimensionArticlesMathematics - Metric GeometryMathematics - Classical Analysis and ODEscircular Furstenberg setClassical Analysis and ODEs (math.CA)FOS: MathematicsulottuvuusFurstenberg setdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-03-27 | Annales Fennici Mathematici |