ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Georgiy Arutyunyants (University of Missouri)
Falconer conjecture, projection theorems and discrete analogs

Abstract: The Falconer conjecture says that if a compact set in R^d has Hausdorff dimension >d/2, then the Euclidean distance set has positive Lebesgue measure. We prove that the conjecture holds on average. Using this we also prove discrete analogs for the asymptotic version of the Erdos distance problem. This is joint work with Alex Iosevich.