幾何セミナー


2017/4/10(Mon)

13:00--14:30 E404

Zoltan Balogh

University of Bern

Geodesic interpolation inequalities on Heisenberg groups

We establish geodesic interpolation inequalities in the sub-Riemannian setting of the Heisenberg group $\mathbb H^n$. 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 Schmuckenschl\"ager. The latter statement implies sub-Riemannian versions of the geodesic Pr\'ekopa-Leindler and Brunn-Minkowski inequalities. The proofs are based on tools of optimal mass transportation showing the power of this method also in case of singular spaces.