Conformal and CR mappings on Carnot groups

Michael G. Cowling; Ji Li; Alessandro Ottazzi; Qingyan Wu

doi:10.1090/bproc/48

Conformal and CR mappings on Carnot groups

Michael G. Cowling, Ji Li, Alessandro Ottazzi, Qingyan Wu

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

6 Downloads (Pure)

Abstract

We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in C^N that induce their CR structure.

Original language	English
Pages (from-to)	67-81
Number of pages	15
Journal	Proceedings of the American Mathematical Society, Series B
Volume	7
DOIs	https://doi.org/10.1090/bproc/48
Publication status	Published - 17 Jun 2020

Bibliographical note

Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Carnot groups
CR mappings
quasiconformal mappings
conformal mappings

Access to Document

10.1090/bproc/48Licence: CC BY-NC

Publisher version (open access)Final published version, 235 KBLicence: CC BY-NC

Cite this

@article{986b0376247f4d218d04c71a59e9cccb,

title = "Conformal and CR mappings on Carnot groups",

abstract = "We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in CN that induce their CR structure.",

keywords = "Carnot groups, CR mappings, quasiconformal mappings, conformal mappings",

author = "Cowling, {Michael G.} and Ji Li and Alessandro Ottazzi and Qingyan Wu",

note = "Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.",

year = "2020",

month = jun,

day = "17",

doi = "10.1090/bproc/48",

language = "English",

volume = "7",

pages = "67--81",

journal = "Proceedings of the American Mathematical Society, Series B",

issn = "2330-1511",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Conformal and CR mappings on Carnot groups

AU - Cowling, Michael G.

AU - Li, Ji

AU - Ottazzi, Alessandro

AU - Wu, Qingyan

N1 - Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2020/6/17

Y1 - 2020/6/17

N2 - We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in CN that induce their CR structure.

AB - We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in CN that induce their CR structure.

KW - Carnot groups

KW - CR mappings

KW - quasiconformal mappings

KW - conformal mappings

UR - http://purl.org/au-research/grants/arc/DP170103025

UR - http://purl.org/au-research/grants/arc/DP170101060

UR - http://www.scopus.com/inward/record.url?scp=85118015157&partnerID=8YFLogxK

U2 - 10.1090/bproc/48

DO - 10.1090/bproc/48

M3 - Article

SN - 2330-1511

VL - 7

SP - 67

EP - 81

JO - Proceedings of the American Mathematical Society, Series B

JF - Proceedings of the American Mathematical Society, Series B

ER -

Conformal and CR mappings on Carnot groups

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this