Dimension estimates on circular (s,t)-Furstenberg sets
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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© 2022 Annales Fennici Mathematici
Tässä työssä osoitetaan, että tason R2Furstenbergin (s,t)-ympyräjoukkojen Hausdorffin ulottuvuus on vähintään max{t3+s,(2t+ 1)s−t} kaikilla 0< s,t≤1. Tämä tulos yleistää Wolffin aiemmin todistamia Kakeyan ympyräjoukkojen ulottuvuusarvioita. In this paper, we show that circular(s,t)-Furstenberg sets in R2 have Hausdorff dimension at least max {t3+s,(2t+ 1)s−t} for all 0< s,t≤1.This result extends the previous dimension estimates on circular Kakeya sets by Wolff.
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