Wasserstein Barycenters Over Heisenberg Group

In this paper, we introduce and investigate Wasserstein barycenters over Heisenberg group. We prove that Wasserstein barycenters always exist over Heisenberg group for measures which is absolutely continuous with (a. c. w) Lebesgue measure \({\mathcal{L}}^{2n + 1}\) . Moreover, our paper shows that such barycenters are unique. Our results extend to the work of Kim and Pass for Riemannian manifolds.