Lipschitz extensions of maps between Heisenberg groups

Balogh, Zoltán M.; Lang, Urs; Pansu, Pierre

doi:10.5802/aif.3046

Lipschitz extensions of maps between Heisenberg groups
[Extensions lipschitziennes d’applications entre groupes d’Heisenberg]

Balogh, Zoltán M.¹ ; Lang, Urs ² ; Pansu, Pierre ³

¹ Department of Mathematics University of Bern Sidlerstrasse 5 CH-3012 Bern, Switzerland
² Department of Mathematics ETH Zürich Rämistrasse 101 CH-8092 Zürich, Switzerland
³ Laboratoire de Mathématiques d’Orsay Univ. Paris-Sud, CNRS, Univ. Paris-Saclay Bâtiment 405 F-91405 Orsay France

Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1653-1665.

Résumé
Abstract

Soit $ℍ^{n}$ le groupe d’Heisenberg de dimension topologique $2 n + 1$ . On montre que si $n$ est impair, le couple d’espaces métriques $(ℍ^{n}, ℍ^{n})$ ne possède pas la propriété d’extension lipschitzienne.

Let $ℍ^{n}$ be the Heisenberg group of topological dimension $2 n + 1$ . We prove that if $n$ is odd, the pair of metric spaces $(ℍ^{n}, ℍ^{n})$ does not have the Lipschitz extension property.

Reçu le : 2015-05-27
Révisé le : 2015-12-15
Accepté le : 2016-01-21
Publié le : 2016-07-28

DOI : 10.5802/aif.3046

Classification : 43A80
Keywords: Heisenberg group, Lipschitz extension property
Mot clés : Groupe d’Heisenberg, propriété d’extension lipschitzienne

Affiliations des auteurs :

Balogh, Zoltán M. ¹ ; Lang, Urs ² ; Pansu, Pierre ³

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Balogh, Zoltán M.; Lang, Urs; Pansu, Pierre. Lipschitz extensions of maps between Heisenberg groups. Annales de l'Institut Fourier, Tome 66 (2016) no. 4, pp. 1653-1665. doi : 10.5802/aif.3046. http://www.numdam.org/articles/10.5802/aif.3046/

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