Given a complete Riemannian manifold M with a lower Ricci curvature bound, we consider barycenters in the Wasserstein space \({\mathcal {W}}_2(M)\) of probability measures on M. We refer to them as Wasserstein barycenters, which by definition are probability measures on M. The goal of this article is to present a novel approach to proving their absolute continuity. We introduce a new class of displacement functionals exploiting the Hessian equality for Wasserstein barycenters. To provide suitable instances of such functionals, we revisit Souslin space theory, Dunford-Pettis theorem and the de la Vallée Poussin criterion for uniform integrability. Our method shows that if a probability measure \({\mathbb {P}}\) on \({\mathcal {W}}_2(M)\) gives mass to absolutely continuous measures on M, then its unique barycenter is also absolutely continuous. This generalizes the previous results on compact manifolds by Kim and Pass [33].
