  Inspired by Y. Ollivier's coarse Ricci curvature, we introduce a novel
concept of coarse extrinsic curvature on Riemannian submanifolds. This is
defined through Wasserstein distances between test probability measures
supported in the tubular neighbourhood of the submanifold. This framework
provides an understanding of the geometric properties of embeddings, offering
valuable insights into their curvature dynamics and intrinsic structures.
Additionally, this coarse curvature can also be extracted from empirical
measures supported on random point clouds generated by a Poisson point process,
and has the potential to extend to metric embeddings.
