 

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 


Abstract
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 δdiscretized 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 606077045
nets@math.uic.edu
http://www.math.uic.edu/~nets/
Terence Tao:
Department of Mathematics, UCLA, Los Angeles CA 900951555
tao@math.ucla.edu
http://www.math.ucla.edu/~tao/

