Gromov's compactness theorem
Encyclopedia
Gromov's compactness theorem can refer to either of two mathematical theorems:
- Gromov's compactness theorem (geometry)Gromov's compactness theorem (geometry)In Riemannian geometry, Gromov's compactness theorem states thatthe 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....
in Riemannian geometry - Gromov's compactness theorem (topology)Gromov's compactness theorem (topology)In symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may have nodes or "bubbles". A bubble is a holomorphic sphere...
in symplectic topology