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 pre-compact in the Gromov-Hausdorff metric. It was proved by Mikhail Gromov.
This theorem is a generalization of the Myers_theorem.