Synthetic versus distributional lower Ricci curvature bounds
| Autor: | Kunzinger, Michael, Oberguggenberger, Michael, Vickers, James A. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154 (2024) 1406-1430 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/prm.2023.70 |
| Popis: | We compare two standard approaches to defining lower Ricci curvature bounds for Riemannian metrics of regularity below $C^2$. 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 $C^1$ and that the converse holds for $C^{1,1}$-metrics under an additional convergence condition on regularisations of the metric. Comment: 23 pages, small correction in the proof of Th. 4.3 |
| Databáze: | arXiv |
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