New York Journal of Mathematics
Volume 7 (2001) 149-187


Nets Hawk Katz and Terence Tao

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

Published: October 17, 2001
Keywords: Falconer distance set conjecture, Furstenberg sets, Hausdorff dimension, Erdös ring conjecture, combinatorial geometry
Subject: 05B99, 28A78, 28A75

In this paper we investigate three unsolved conjectures in geometric 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 conjectures and show that in a certain sense that these discretized versions are equivalent.

Author information

Nets Hawk Katz:
Department of Mathematics, University of Illinois at Chicago, Chicago IL 60607-7045

Terence Tao:
Department of Mathematics, UCLA, Los Angeles CA 90095-1555