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 language | English (US) |
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Pages (from-to) | 569-604 |
Number of pages | 36 |
Journal | Advances in Mathematics |
Volume | 231 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1 2012 |
Keywords
- Hausdorff dimension
- Heisenberg group
- Isotropic Grassmannian
- Potential theory
- Projection
ASJC Scopus subject areas
- General Mathematics