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Coarse Ricci curvature of weighted Riemannian manifolds | Synapse

February 9, 2026

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Coarse Ricci curvature of weighted Riemannian manifolds

Puntos clave

The aim is to understand how the generalized Ricci tensor can be estimated in weighted Riemannian manifolds using Wasserstein distances.
Analyzed the generalized Ricci tensor in weighted complete Riemannian manifolds.
Utilized scaled metric derivatives of Wasserstein 1-distances.
Applied findings to random geometric graphs from Poisson point processes.
Demonstrated asymptotic retrieval of generalized Ricci tensor from metric derivatives.
Showed convergence of coarse curvature in graphs to the generalized Ricci tensor.

Resumen

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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Cite This Study

Arnaudon et al. (Tue,) studied this question.

synapsesocial.com/papers/698979e9f0ec2af6756e7fa8 https://doi.org/https://doi.org/10.1090/tran/9482

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