Gromov's compactness theorem (geometry)


In Riemannian geometry, Gromov's 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.