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

Jiayin Liu

Type: Article

Publication Date: 2023-03-27

Citations: 0

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

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.

Locations

Annales Fennici Mathematici - View - PDF
arXiv (Cornell University) - View - PDF
Jyväskylä University Digital Archive (University of Jyväskylä) - View - PDF

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Works Cited by This (12)

Action	Title	Year	Authors
+ PDF Chat	Recent work connected with the Kakeya problem	2003	Thomas Wolff
+	A Kakeya-type problem for circles	1997	Thomas Wolff
+ PDF Chat	Local smoothing type estimates on Lp for large p	2000	Thomas Wolff
+ PDF Chat	Furstenberg sets for a fractal set of directions	2011	Ursula Molter Ezequiel Rela
+ PDF Chat	On continuum incidence problems related to harmonic analysis	2003	Wilhelm Schlag
+	Some connections between Falconer's distance set conjecture, and sets of Furstenburg type	2001	Nets Hawk Katz Terence Tao
+ PDF Chat	Hausdorff dimension of unions of affine subspaces and of Furstenberg-type sets	2019	Kornélia Héra Tamás Keleti András Máthé
+	Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces	2019	Kornélia Héra
+ PDF Chat	On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane	2023	Tuomas Orponen Pablo Shmerkin
+	Integrability of orthogonal projections, and applications to Furstenberg sets	2022	Damian Dąbrowski Tuomas Orponen Michele Villa