A Survey on the Hausdorff Dimension of Intersections

Abstract

Let A and B be Borel subsets of the Euclidean n-space with $dimA+dimB>n$. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections $A\cap \left(g\right(B)+z)$ for generic orthogonal transformations g and translations by z?