Corpus ID: 119734780

Remarks about Synthetic Upper Ricci Bounds for Metric Measure Spaces

@article{Sturm2017RemarksAS,
  title={Remarks about Synthetic Upper Ricci Bounds for Metric Measure Spaces},
  author={Karl-Theodor Sturm},
  journal={arXiv: Differential Geometry},
  year={2017}
}
We discuss various characterizations of synthetic upper Ricci bounds for metric measure spaces in terms of heat flow, entropy and optimal transport. In particular, we present a characterization in terms of semiconcavity of the entropy along certain Wasserstein geodesics which is stable under convergence of mm-spaces. And we prove that a related characterization is equivalent to an asymptotic lower bound on the growth of the Wasseretein distance between heat flows. For weighted Riemannian… Expand
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