Gromov's compactness theorem (geometry)

In Riemannian geometry, Gromov's (pre)compactness theorem states that the set of compact Riemannian manifolds of a given dimension, with Ricci curvature ≥ c and diameter ≤ D is relatively compact in the Gromov–Hausdorff metric. It was proved by Mikhail Gromov in 1981.

This theorem is a generalization of Myers's theorem.