JournalsrmiVol. 30, No. 2pp. 463–476

Transversality of isotropic projections, unrectifiability, and Heisenberg groups

  • Risto Hovila

    University of Helsinki, Finland
Transversality of isotropic projections, unrectifiability, and Heisenberg groups cover
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Abstract

We show that the family of mm-dimensional isotropic projections in R2n\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 ER2nE \subset \mathbb{R}^{2n}. These results may also be applied to gain information on the horizontal projections of the Heisenberg group Hn\mathbb{H}^n.

Cite this article

Risto Hovila, Transversality of isotropic projections, unrectifiability, and Heisenberg groups. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 463–476

DOI 10.4171/RMI/789