Projection and slicing theorems in Heisenberg groups

Zoltán M. Balogh, Katrin Fässler, Pertti Mattila, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

We study the behavior of the Hausdorff dimension of sets in the Heisenberg group Hn, n∈N, with a sub-Riemannian metric under projections onto horizontal and vertical subgroups, and under slicing by translates of vertical subgroups. We formulate almost sure statements in terms of a natural measure on the Grassmannian of isotropic subspaces.

Original languageEnglish (US)
Pages (from-to)569-604
Number of pages36
JournalAdvances in Mathematics
Volume231
Issue number2
DOIs
StatePublished - Oct 1 2012

Keywords

  • Hausdorff dimension
  • Heisenberg group
  • Isotropic Grassmannian
  • Potential theory
  • Projection

ASJC Scopus subject areas

  • Mathematics(all)

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