108 citations · 378 across the 31 of their papers we have counts for
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math.CA2006★ 4 cited
Kakeya Sets in Cantor directions
Michael D. Bateman, Nets Hawk Katz
We construct a union of N parallelograms of dimensions approximately 1/N x 1 in the plane, with the slope of their long sides in the standard Cantor set. The union has area 1/log N…
math.CA2006★ 1 cited
On Sums, Products, and the multidimensional Falconer problem
Nets Hawk Katz
A set in d dimensional Euclidean space with d larger than 2 having Hausdorff dimension at least d/2 must have distance set with Hausdorff dimension strictly greater than 1/2.