Inserted: 16 dec 2014
Last Updated: 16 dec 2014
Journal: Calculus of Variations
We show that the configuration space Υ over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies a lower Ricci curvature bound on Υ in the sense of Lott–Sturm–Villani, the Bochner inequality, gradient estimates and Wasserstein contraction. Moreover, we show that the heat flow on Υ can be identified as the gradient flow of the entropy.