Curvature bounds for configuration spaces

  • Matthias Erbar
  • Martin Huesmann


We show that the configuration space \(\Upsilon \) 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 \(\Upsilon \) in the sense of Lott–Sturm–Villani, the Bochner inequality, gradient estimates and Wasserstein contraction. Moreover, we show that the heat flow on \(\Upsilon \) can be identified as the gradient flow of the entropy.



The authors would like to thank Theo Sturm and Fabio Cavalletti for several fruitful discussions on the subject of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute for Applied MathematicsUniversity of BonnBonnGermany

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