no. 9
Geometry
Geodesic interpolation inequalities on Heisenberg groups
[Inégalités d'interpolation géodésique sur les groupes de Heisenberg]

Présenté par : Philippe G. Ciarlet

Balogh, Zoltán M.1 ; Kristály, Alexandru2, 3 ; Sipos, Kinga1
1 Mathematisches Institute, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
2 Institute of Applied Mathematics, Óbuda University, Budapest, Hungary
3 Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania
Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 916-919.

Dans cette Note, nous présentons des versions géodésiques des inégalités de Borell–Brascamp–Lieb et de Brunn–Minkowski, et des inégalités d'entropie sur le groupe de Heisenberg Hn. Nos démonstrations s'appuient sur l'approximation riemannienne de Hn et sur des techniques de transport optimal.

In this Note, we present geodesic versions of the Borell–Brascamp–Lieb, Brunn–Minkowski and entropy inequalities on the Heisenberg group Hn. Our arguments use the Riemannian approximation of Hn combined with optimal mass-transportation techniques.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.07.001
Balogh, Zoltán M. 1 ; Kristály, Alexandru 2, 3 ; Sipos, Kinga 1

1 Mathematisches Institute, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
2 Institute of Applied Mathematics, Óbuda University, Budapest, Hungary
3 Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania 
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Balogh, Zoltán M.; Kristály, Alexandru; Sipos, Kinga. Geodesic interpolation inequalities on Heisenberg groups. Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 916-919. doi : 10.1016/j.crma.2016.07.001. http://www.numdam.org/articles/10.1016/j.crma.2016.07.001/

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