… We prove analogs of classical almost sure dimension theorems for Euclidean projection
mappings in the first Heisenberg group, equipped with a sub-Riemannian metric. … In this
paper, we study projection mappings from the Heisenberg group onto horizontal lines and
complementary vertical planes. In particular we consider the effect of such mappings on the
Hausdorff dimensions and Hausdorff measure of subsets of the Heisenberg group
considered with respect to a sub-Riemannian metric. Our results are analogs, in sub-Riemannian …