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   \(\max\{\tfrac{t}3+s,(2t+1)s-t\}\) for all \(0<s,t\le 1\).   This result extends the previous dimension estimates on circular Kakeya sets by Wolff.