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
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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, 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: |
05 Dec 2022 15:25 |
Publisher DOI: |
10.1007/s00526-018-1320-3 |
BORIS DOI: |
10.7892/boris.125484 |
URI: |
https://boris.unibe.ch/id/eprint/125484 |
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