Improving dimension estimates for Furstenberg-type sets

Abstract

In this paper we prove some lower bounds on the Hausdorff dimension of sets of Furstenberg type. Moreover, we extend these results to sets of generalized Furstenberg type, associated to doubling dimension functions. With some additional growth conditions on the dimension function, we obtain a lower bound on the dimension of "zero dimensional" Furstenberg sets.

16 pages, 3 figures

References in corpus (2)

• From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE
• Some connections between Falconer's distance set conjecture, and sets of Furstenburg type