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A relatively simple proof of the theorem was found by Bruce Kleiner. [5] Later, Terence Tao and Yehuda Shalom modified Kleiner's proof to make an essentially elementary proof as well as a version of the theorem with explicit bounds. [6] [7] Gromov's theorem also follows from the classification of approximate groups obtained by Breuillard, Green ...
Download as PDF; Printable version; In other projects ... Gromov's theorem may mean one of a number of results of Mikhail Gromov: One of Gromov's compactness theorems
The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. [1] It was first proven in 1985 by Mikhail Gromov. [2] The theorem states that one cannot embed a ball into a cylinder via a symplectic map unless the radius of the ball is less than or equal to the radius of the ...
Print/export Download as PDF; Printable version; In other projects ... Gromov's theorem on groups of polynomial growth; Growth rate (group theory) H.
The role of this theorem in the theory of Gromov–Hausdorff convergence may be considered as analogous to the role of the Arzelà–Ascoli theorem in the theory of uniform convergence. [2] Gromov first formally introduced it in his 1981 resolution of the Milnor–Wolf conjecture in the field of geometric group theory , where he applied it to ...
Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Gromov's compactness theorem (geometry) H. Hopf–Rinow theorem; K.
Gromov used this theory to prove a non-squeezing theorem concerning symplectic embeddings of spheres into cylinders. Gromov showed that certain moduli spaces of pseudoholomorphic curves (satisfying additional specified conditions) are compact , and described the way in which pseudoholomorphic curves can degenerate when only finite energy is ...
In the mathematical field of 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 (a finite tree of) "bubbles". A bubble is a holomorphic sphere which ...