Publication

Coarse Ricci Curvature of Weighted Riemannian Manifolds

Xue-Mei Li-Hairer
2025

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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Coarse Ricci Curvature of Weighted Riemannian Manifolds

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