Revista Matemática Iberoamericana


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Volume 30, Issue 2, 2014, pp. 463–476
DOI: 10.4171/RMI/789

Published online: 2014-07-08

Transversality of isotropic projections, unrectifiability, and Heisenberg groups

Risto Hovila[1]

(1) University of Helsinki, Finland

We show that the family of $m$-dimensional isotropic projections in $\mathbb{R}^{2n}$ 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 $E \subset \mathbb{R}^{2n}$. These results may also be applied to gain information on the horizontal projections of the Heisenberg group $\mathbb{H}^n$.

Keywords: Projection, symplectic geometry, Hausdorff dimension, Heisenberg group, unrectifiability

Hovila Risto: Transversality of isotropic projections, unrectifiability, and Heisenberg groups. Rev. Mat. Iberoam. 30 (2014), 463-476. doi: 10.4171/RMI/789