Frequency of Sobolev dimension distortion of horizontal subgroups in Heisenberg groups

Balogh, Zoltan; Tyson, Jeremy; Wildrick, Kevin Michael (2017). Frequency of Sobolev dimension distortion of horizontal subgroups in Heisenberg groups. Annali della Scuola normale superiore di Pisa - classe di scienze, 17(2), pp. 655-683. Scuola normale superiore di Pisa 10.2422/2036-2145.201409_08

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We study the behavior of Sobolev mappings 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 mappings. Our approach unifies ideas of Gehring and Mostow about the absolute continuity of quasiconformal mappings withMattila’s projection and slicing machinery.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan; Tyson, Jeremy and Wildrick, Kevin Michael

Subjects:

500 Science > 510 Mathematics

ISSN:

0391-173X

Publisher:

Scuola normale superiore di Pisa

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 09:57

Last Modified:

17 Apr 2018 09:57

Publisher DOI:

10.2422/2036-2145.201409_08

BORIS DOI:

10.7892/boris.109135

URI:

https://boris.unibe.ch/id/eprint/109135

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