Transversality of isotropic projections, unrectifiability and Heisenberg groups

2012/05/14 by Hovila, Risto · 2 citations
#28A78 #28A80 #53D05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.3010

Abstract

We show that the family of m-dimensional isotropic projections in \R²ⁿ 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 ⊂ \R²ⁿ. These results may also be applied to gain information on the horizontal projections of the Heisenberg group \Hⁿ.

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• Besicovitch-Federer projection theorem for measures
• Strong exceptional parameters for the dimension of nonlinear slices

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