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  2. Gromov's theorem on groups of polynomial growth - Wikipedia

    en.wikipedia.org/wiki/Gromov's_theorem_on_groups...

    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 ...

  3. Gromov's theorem - Wikipedia

    en.wikipedia.org/wiki/Gromov's_theorem

    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

  4. Non-squeezing theorem - Wikipedia

    en.wikipedia.org/wiki/Non-squeezing_theorem

    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 ...

  5. Category:Metric geometry - Wikipedia

    en.wikipedia.org/wiki/Category:Metric_geometry

    Print/export Download as PDF; Printable version; In other projects ... Gromov's theorem on groups of polynomial growth; Growth rate (group theory) H.

  6. Gromov's compactness theorem (geometry) - Wikipedia

    en.wikipedia.org/wiki/Gromov's_compactness...

    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 ...

  7. Category:Theorems in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in...

    Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Gromov's compactness theorem (geometry) H. Hopf–Rinow theorem; K.

  8. Pseudoholomorphic curve - Wikipedia

    en.wikipedia.org/wiki/Pseudoholomorphic_curve

    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 ...

  9. Gromov's compactness theorem (topology) - Wikipedia

    en.wikipedia.org/wiki/Gromov's_compactness...

    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 ...