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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 Wikidata item; ... Gromov's theorem on groups of polynomial growth; Grushko theorem; H.
Print/export Download as PDF; Printable version; In other projects ... Gromov's theorem on groups of polynomial growth; Growth rate (group theory) H.
The Tits alternative is an important ingredient [2] in the proof of Gromov's theorem on groups of polynomial growth. In fact the alternative essentially establishes the result for linear groups (it reduces it to the case of solvable groups, which can be dealt with by elementary means).
Print/export Download as PDF; Printable version; In other projects ... Gromov boundary; Gromov's theorem on groups of polynomial growth;
This fact is a special case of the general theorem of Hyman Bass and Yves Guivarch that is discussed in the article on Gromov's theorem. The lamplighter group has an exponential growth. The existence of groups with intermediate growth, i.e. subexponential but not polynomial was open for many years.