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

Authors

  • Jiayin Liu University of Jyväskylä, Department of Mathematics and Statistics

DOI:

https://doi.org/10.54330/afm.128073

Keywords:

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.

Downloads

Published

2023-03-27

Issue

Vol. 48 No. 1 (2023)

Section

Articles

License

Copyright (c) 2022 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

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