Can we learn the curvature of a data manifold from a finite sample? We study continuum limits of Ollivier’s Ricci curvature on geometric graphs, proving pointwise consistency and showing that positive lower bounds on the underlying manifold are inherited by the graph with high probability. We further discuss applications to heat kernels and manifold learning.
With Nicolás García Trillos. Now published in Discrete & Computational Geometry: https://link.springer.com/article/10.1007/s00454-026-00839-5