= Gromov's compactness theorem (geometry)
{wiki=Gromov's_compactness_theorem_(geometry)}
Gromov's compactness theorem, often referred to in the context of many areas in geometric analysis and differential geometry, primarily deals with the compactness of certain collections of Riemannian manifolds. It provides a criterion for when a sequence of Riemannian manifolds can be shown to converge in a meaningful way. The theorem applies to families of Riemannian manifolds that are uniformly bounded in terms of geometry, meaning they satisfy certain bounds on curvature, diameter, and volume.
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