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arXiv · 2303.04228

Coarse Ricci curvature of weighted Riemannian manifolds

Marc Arnaudon·Xue-Mei Li·Benedikt Petko
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Abstract

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.

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Marc Arnaudon, Xue-Mei Li, Benedikt Petko. 2023-03-07. Coarse Ricci curvature of weighted Riemannian manifolds. https://arxiv.org/abs/2303.04228

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