Gromov's compactness theorem (geometry)

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For Gromov's compactness theorem in symplectic topology, see that article.

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.