Geometric inequalities on Heisenberg groups

Balogh, Zoltan; Kristály, Alexandru; Sipos, Kinga (2018). Geometric inequalities on Heisenberg groups. Calculus of variations and partial differential equations, 57(2) Springer 10.1007/s00526-018-1320-3

[img]
Preview
Text
Balogh2018_Article_GeometricInequalitiesOnHeisenb.pdf - Published Version
Available under License Creative Commons: Attribution (CC-BY).

Download (838kB) | Preview

We establish geometric inequalities in the sub-Riemannian setting of the Heisenberg group Hⁿ. Our results include a natural sub-Riemannian version of the celebrated curvature-dimension condition of Lott–Villani and Sturm and also a geodesic version of the Borell–Brascamp–Lieb inequality akin to the one obtained by Cordero-Erausquin, McCann and Schmuckenschläger. The latter statement implies sub-Riemannian versions of the geodesic Prékopa–Leindler and Brunn–Minkowski inequalities. The proofs are based on optimal mass transportation and Riemannian approximation of Hⁿ developed by Ambrosio and Rigot. These results refute a general point of view, according to which no geometric inequalities can be derived by optimal mass transportation on singular spaces.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan and Sipos, Kinga

Subjects:

500 Science > 510 Mathematics

ISSN:

0944-2669

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

10 May 2019 14:27

Last Modified:

24 Oct 2019 20:10

Publisher DOI:

10.1007/s00526-018-1320-3

BORIS DOI:

10.7892/boris.125484

URI:

https://boris.unibe.ch/id/eprint/125484

Actions (login required)

Edit item Edit item
Provide Feedback