 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.