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Falconer distance problem, additive energy and Cartesian products
A celebrated result due to Wolff says if is a compact subset of , then the Lebesgue measure of the distance set is positive if the Hausdorff dimension of is greater than
. In this paper we improve the barrier by a small
exponent for Cartesian products. In higher dimensions, also in the context of
Cartesian products, we reduce Erdogan's exponent to
. The proof uses a combination of Fourier analysis and
additive comibinatorics.Comment: 9 page
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