Coarse Ricci curvature of weighted Riemannian manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866915232703578112 |
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| author | Arnaudon, Marc Li, Xue-Mei Petko, Benedikt |
| author_facet | Arnaudon, Marc Li, Xue-Mei Petko, Benedikt |
| contents | We show that the generalized Ricci tensor of a weighted complete Riemannian manifold can be retrieved asymptotically from a scaled metric derivative of Wasserstein 1-distances between normalized weighted local volume measures. As an application, we demonstrate that the limiting coarse curvature of random geometric graphs sampled from Poisson point process with non-uniform intensity converges to the generalized Ricci tensor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04228 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Coarse Ricci curvature of weighted Riemannian manifolds Arnaudon, Marc Li, Xue-Mei Petko, Benedikt Differential Geometry Combinatorics Probability 53B21 (Primary) 60D05, 05C80 (Secondary) We show that the generalized Ricci tensor of a weighted complete Riemannian manifold can be retrieved asymptotically from a scaled metric derivative of Wasserstein 1-distances between normalized weighted local volume measures. As an application, we demonstrate that the limiting coarse curvature of random geometric graphs sampled from Poisson point process with non-uniform intensity converges to the generalized Ricci tensor. |
| title | Coarse Ricci curvature of weighted Riemannian manifolds |
| topic | Differential Geometry Combinatorics Probability 53B21 (Primary) 60D05, 05C80 (Secondary) |
| url | https://arxiv.org/abs/2303.04228 |