Geometric inequalities on Heisenberg groups

• DOI: 10.1007/s00526-018-1320-3
• Publication Date: 2018-03-13T09:12:31Z
• Authors: Zoltán M. Balogh; Alexandru Kristály; Kinga Sipos
• Keywords: Heisenberg group; Statement (logic)

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