Some Connections between Falconer's Distance Set Conjecture and Sets of Furstenburg Type

摘要

In this paper we investigate three unsolved conjectures ingeometric combinatorics, namely Falconer's distance set conjecture,the dimension of Furstenburg sets, and Erdös's ring conjecture.We formulate natural δ-discretized versions of these conjecturesand show that in a certain sense that these discretized versions areequivalent.