Geodesic interpolation inequalities on Heisenberg groups (Q309763)

In the short note under review, the authors state and sketch the proofs of geodesic versions of the Borell-Brascamp-Lieb, Brunn-Minkowski and entropy inequalities on the Heisenberg group \(\mathbb H^n\). Their methods rely on the use of Riemannian approximations of \(\mathbb H^n\), combined with optimal mass transportation techniques. Detailed proofs, further results and comments are deferred to a longer preprint.