Curvature bounds for configuration space

Erbar Matthias - Huesmann Martin

year: 2014
journal: Calculus of Variations
abstract: 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.

The paper is available on the cvgmt preprint server.