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Nets Hawk Katz and Terence Tao
Some Connections between Falconer's Distance Set Conjecture and Sets of Furstenburg Type
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| Published: |
October 17, 2001
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| Keywords: |
Falconer distance set conjecture, Furstenberg sets, Hausdorff dimension, Erdös ring conjecture, combinatorial geometry |
| Subject: |
05B99, 28A78, 28A75 |
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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.
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| 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/
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