Search results
Results from the WOW.Com Content Network
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 ...
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 ...
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 Riemannian geometry; Gromov's compactness theorem (topology) in symplectic topology; Gromov's Betti number theorem Gromov–Ruh theorem on almost flat manifolds
In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry.
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).
Grinberg's theorem (graph theory) Gromov's compactness theorem (Riemannian geometry) Gromov's compactness theorem (symplectic topology) Gromov's theorem on groups of polynomial growth (geometric group theory) Gromov–Ruh theorem (differential geometry) Gross–Zagier theorem (number theory)
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.
Gromov's almost flat manifolds. Astérisque, 81. Société Mathématique de France, Paris, 1981. 148 pp. Peter Buser and Hermann Karcher. The Bieberbach case in Gromov's almost flat manifold theorem. Global differential geometry and global analysis (Berlin, 1979), pp. 82–93, Lecture Notes in Math., 838, Springer, Berlin-New York, 1981.