Comptes Rendus
no. 9
Geometry
Geodesic interpolation inequalities on Heisenberg groups

Presented by: Philippe G. Ciarlet

Zoltán M. Balogh1; Alexandru Kristály2, 3; Kinga Sipos1
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, Volume 354 (2016) no. 9, pp. 916-919.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.07.001

Zoltán M. Balogh 1; Alexandru Kristály 2, 3; Kinga Sipos 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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Zoltán M. Balogh; Alexandru Kristály; Kinga Sipos. Geodesic interpolation inequalities on Heisenberg groups. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 916-919. doi : 10.1016/j.crma.2016.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.001/

[1] L. Ambrosio; S. Rigot Optimal mass transportation in the Heisenberg group, J. Funct. Anal., Volume 208 (2004) no. 2, pp. 261-301

[2] Z.M. Balogh; A. Kristály; K. Sipos Geometric inequalities on Heisenberg groups, 2016 | arXiv

[3] D. Cordero-Erausquin; R.J. McCann; M. Schmuckenschläger A Riemannian interpolation inequality à la Borell, Brascamp and Lieb, Invent. Math., Volume 146 (2001) no. 2, pp. 219-257

[4] A. Figalli; N. Juillet Absolute continuity of Wasserstein geodesics in the Heisenberg group, J. Funct. Anal., Volume 255 (2008) no. 1, pp. 133-141

[5] A. Figalli; L. Rifford Mass transportation on sub-Riemannian manifolds, Geom. Funct. Anal., Volume 20 (2010), pp. 124-159

[6] N. Juillet Geometric inequalities and generalized Ricci bounds in the Heisenberg group, Int. Math. Res. Not., Volume 13 (2009)

[7] J. Lott; C. Villani Ricci curvature for metric measure spaces via optimal transport, Ann. Math., Volume 169 (2009) no. 3, pp. 903-991

[8] J. McCann Polar factorization of maps in Riemannian manifolds, Geom. Funct. Anal., Volume 11 (2001), pp. 589-608

[9] K.-T. Sturm On the geometry of metric measure spaces. I, Acta Math., Volume 196 (2006) no. 1, pp. 65-131

[10] K.-T. Sturm On the geometry of metric measure spaces. II, Acta Math., Volume 196 (2006) no. 1, pp. 133-177

[11] C. Villani Optimal Transport. Old and New, Fundamental Principles of Mathematical Sciences, vol. 338, Springer-Verlag, Berlin, 2009

[12] C. Villani Topics in Optimal Transportation, American Mathematical Society, Providence, RI, USA, 2003

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