Riemannian manifolds are relatively compact in the Gromov-Hausdorff metric Gromov's compactness theorem (topology) on the existence of limits of sequences...

In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex...

Gromov's theorem may mean one of a number of results of Mikhail Gromov: One of Gromov's compactness theorems: Gromov's compactness theorem (geometry) in...

was later reformulated by Gromov and others into the more flexible notion of an ultralimit.[G93] Gromov's compactness theorem had a deep impact on the...

converges in the pointed Gromov–Hausdorff sense. Another simple and very useful result in Riemannian geometry is Gromov's compactness theorem, which states that...

Gauss–Bonnet theorem (differential geometry) Geroch's splitting theorem (differential geometry) Gromov's compactness theorem (Riemannian geometry) Gromov's compactness...

Cheeger and Mikhael Gromov's theorem characterizing collapsing manifolds. In Perelman's adaptation, he required use of a new theorem characterizing manifolds...

practice, topology often means dealing with large-scale properties of spaces, such as connectedness and compactness. The field of topology, which saw...

and co-authors, which uses Thurston's hyperbolization theorem for Haken manifolds and Gromov's norm for 3-manifolds. A book by the same authors with complete...

not be minima). In the Hopf–Rinow theorem, the first characterization of completeness deals purely with the topology of the manifold and the boundedness...

Gromov's compactness theorem. The set of all Riemannian manifolds with positive Ricci curvature and diameter at most D is pre-compact in the Gromov-Hausdorff...

distance r {\displaystyle r} before diverging. This topology makes the Gromov boundary into a compact metrizable space. The number of ends of a hyperbolic...

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped...

Uniformization theorem Myers theorem Gromov's compactness theorem Gauss–Codazzi equations Darboux frame Hypersurface Induced metric Nash embedding theorem minimal...

3-manifolds M 1 # M 2 {\displaystyle M_{1}\#M_{2}} . In fact, from general theorems in topology, we find for a three manifold with a connected sum decomposition...

1995, Hamilton extended Jeff Cheeger's compactness theory for Riemannian manifolds to give a compactness theorem for sequences of Ricci flows.[H95a] Given...

Gromov, a prominent developer of geometric group theory, inventor of homotopy principle, introduced Gromov's compactness theorem, Gromov norm, Gromov...

Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several...

is discrete if its induced topology is the discrete topology. Although many concepts, such as completeness and compactness, are not interesting for such...

In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations...

satisfies an analogue of Gödel's completeness theorem. Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of...

July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields...

-compatible). This Gromov compactness theorem, now greatly generalized using stable maps, makes possible the definition of Gromov–Witten invariants, which...

computed using Gromov's theory of pseudoholomorphic curves. Unlike Riemannian manifolds, symplectic manifolds are not very rigid: Darboux's theorem shows that...

of the hyperbolic geometry of a 3-manifold to its topology also comes from the Mostow rigidity theorem, which states that the hyperbolic structure of a...

Gromov (1981) gave an alternate proof using the Gromov norm. Besson, Courtois & Gallot (1996) gave the simplest available proof. While the theorem shows...

ISBN 978-1-59593-705-6. See theorem 2.1 in these notes. GROMOV, M. (1990). "CONVEX SETS AND KÄHLER MANIFOLDS". Advances in Differential Geometry and Topology. WORLD SCIENTIFIC...

Mikhail Gromov (1987). The inspiration came from various existing mathematical theories: hyperbolic geometry but also low-dimensional topology (in particular...

Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial...

of mathematics, Preissmann's theorem is a statement that restricts the possible topology of a negatively curved compact Riemannian manifold. It is named...