We study the behavior of Sobolev mApplngs defined on the sub-Riemannian Heisenberg groups with respect to foliations by left cosets of a horizontal homogeneous subgroup. Our main result provides a quantitative estimate, in terms of Hausdorff dimension, of the size of the set of cosets whose dimension is raised under such mApplngs. Our approach unifies ideas of Gehring and Mostow about the absolute continuity of quasiconformal mApplngs with Manila's projection and slicing machinery.
|Original language||English (US)|
|Number of pages||29|
|Journal||Annali della Scuola Normale Superiore di Pisa - Classe di Scienze|
|State||Published - Jan 1 2017|
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (miscellaneous)