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

Författare

  • Jiayin Liu University of Jyväskylä, Department of Mathematics and Statistics
DOI: https://doi.org/10.54330/afm.128073

Nyckelord:

Furstenberg set, circular Furstenberg set, Hausdorff dimension

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.
Nummer
Vol 48 Nr 1 (2023)
Sektion
Articles

Publicerad

2023-03-27

Referera så här

Liu, J. (2023). Dimension estimates on circular (s,t)-Furstenberg sets. Annales Fennici Mathematici, 48(1), 299–324. https://doi.org/10.54330/afm.128073

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