Title
Synthetic versus distributional lower Ricci curvature bounds
Abstract
We compare two standard approaches to defining lower Ricci curvature bounds for Riemannian metrics of regularity below C2. These are, on the one hand, the synthetic definition via weak displacement convexity of entropy functionals in the framework of optimal transport, and the distributional one based on non-negativity of the Ricci-tensor in the sense of Schwartz. It turns out that distributional bounds imply entropy bounds for metrics of class C1 and that the converse holds for C1,1-metrics under an additional convergence condition on regularizations of the metric.
Keywords
low regularityoptimal transportRicci curvature boundssynthetic geometrytensor distributions
Object type
Language
English [eng]
Persistent identifier
phaidra.univie.ac.at/o:2067029
Appeared in
Title
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
ISSN
0308-2105
Issued
2023
From page
1
To page
25
Publication
Cambridge University Press (CUP)
Version type
Date issued
2023
Access rights
Rights
Rights statement
© The Author(s), 2023
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