Hausdorff dimension, intersections of projections and exceptional plane sections (Q2809197)

Let \(G(n,m)\) be the Grassmannian of \(m\)-dimensional linear subspaces in \({\mathbb R}^n\), and \(\gamma_{n,m}\) is the Haar measure on \(G(n,m)\). Let \(A\) and \(B\) be Borel subsets of \({\mathbb R}^n\), and \(P_{V}\), \(P_{V}(B)\) are their orthogonal projections on a linear subspace \(V\). The authors estimate the Haar measures of sets of subspaces \(V\) such that the Hausdorff measure of the intersection \(P_{V}(A)\cap P_{V}(B)\) is positive, or this intersection has a non-empty interior, and so on.