no. 4
Lipschitz extensions of maps between Heisenberg groups
[Extensions lipschitziennes d’applications entre groupes d’Heisenberg]
Balogh, Zoltán M.1 ; Lang, Urs2 ; Pansu, Pierre3
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.

Soit ℍ n le groupe d’Heisenberg de dimension topologique 2n+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 2n+1. We prove that if n is odd, the pair of metric spaces (ℍ n ,ℍ n ) does not have the Lipschitz extension property.

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DOI : 10.5802/aif.3046
Classification : 43A80
Keywords: Heisenberg group, Lipschitz extension property
Mot clés : Groupe d’Heisenberg, propriété d’extension lipschitzienne

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 
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     title = {Lipschitz extensions of maps between {Heisenberg} groups},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3046/

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