|
| 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 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 nets@math.uic.edu http://www.math.uic.edu/~nets/ Terence Tao: Department of Mathematics, UCLA, Los Angeles CA 90095-1555 tao@math.ucla.edu http://www.math.ucla.edu/~tao/ |