Dimension estimates on circular (s,t)-Furstenberg sets

Abstract

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