A gradient-flow proof yields Wasserstein Jensen's inequality, barycenter well-posedness on RCD and extended metric measure spaces, and a new Barycenter-Curvature-Dimension condition with stability and geometric applications.
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On the geometry of Wasserstein barycenter I
A gradient-flow proof yields Wasserstein Jensen's inequality, barycenter well-posedness on RCD and extended metric measure spaces, and a new Barycenter-Curvature-Dimension condition with stability and geometric applications.