Yuki Takahashi


UC Irvine


Tuesday, April 26, 2016 - 1:00pm to 2:00pm

We show that for any two homogeneous Cantor sets with sum of Hausdorff dimensions that exceeds 1, one can create an interval in the sumset by applying arbitrary small perturbations (without leaving the class of homogeneous Cantor sets). We will also discuss the connection of this problem with the question on properties of one dimensional self-similar sets with overlaps.