Gromov's compactness theorem (geometry)

This article is about Gromov's compactness theorem in Riemannian geometry. For Gromov's compactness theorem in symplectic topology, see Gromov's compactness theorem (topology).

In Riemannian geometry, Gromov's (pre)compactness theorem states that the set of 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.

This theorem is a generalization of the Myers theorem.