We show that the family of -dimensional isotropic projections in is transversal. As an application we show that the Besicovitch–Federer projection theorem holds for isotropic projections. We also use transversality to obtain almost sure estimates on the Hausdorff dimension of isotropic projections of subsets . These results may also be applied to gain information on the horizontal projections of the Heisenberg group .
Cite this article
Risto Hovila, Transversality of isotropic projections, unrectifiability, and Heisenberg groups. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 463–476DOI 10.4171/RMI/789