Mathematics – Classical Analysis and ODEs
Scientific paper
2001-01-23
Mathematics
Classical Analysis and ODEs
42 pages, 5 figures, submitted, New York Journal of Mathematics
Scientific paper
In this paper we investigate three unsolved conjectures in geometric combinatorics, namely Falconer's distance set conjecture, the dimension of Furstenburg sets, and Erdos's ring conjecture. We formulate natural $\delta$-discretized versions of these conjectures and show that in a certain sense that these discretized versions are equivalent. In particular, it appears that to progress on any of these problems one must prove a quantitative statement about the existence of sub-rings of $R$ of dimension 1/2.
Katz Nets Hawk
Tao Terence
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