Gromov's compactness theorem (geometry)
On when a set of compact Riemannian manifolds of a given dimension is relatively compact / From Wikipedia, the free encyclopedia
Not to be confused with Gromov's compactness theorem in symplectic geometry.
In the mathematical field of metric geometry, Mikhael Gromov proved a fundamental compactness theorem for sequences of metric spaces. In the special case of Riemannian manifolds, the key assumption of his compactness theorem is automatically satisfied under an assumption on Ricci curvature. These theorems have been widely used in the fields of geometric group theory and Riemannian geometry.