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- Non-squeezing_theorem abstract "The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven in 1985 by the winner of the 2009 Abel Prize, Mikhail Gromov. The theorem states that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder. The importance of this theorem is as follows: very little was known about the geometry behind symplectic transformations. One easy consequence of a transformation being symplectic is that it preserves volume. Since one can easily embed a ball of any radius into a cylinder of any other radius by a volume-preserving transformation: just picture squeezing the ball into the cylinder (hence, the name non-squeezing theorem). Thus, the non-squeezing theorem tells us that, although symplectic transformations are volume preserving, it is much more restrictive for a transformation to be symplectic than it is to be volume preserving.".
- Non-squeezing_theorem wikiPageExternalLink 1208.5969v1.
- Non-squeezing_theorem wikiPageExternalLink ewmcambrevjn23.pdf.
- Non-squeezing_theorem wikiPageID "23825035".
- Non-squeezing_theorem wikiPageRevisionID "598212275".
- Non-squeezing_theorem hasPhotoCollection Non-squeezing_theorem.
- Non-squeezing_theorem subject Category:Symplectic_geometry.
- Non-squeezing_theorem subject Category:Theorems_in_geometry.
- Non-squeezing_theorem type Abstraction100002137.
- Non-squeezing_theorem type Communication100033020.
- Non-squeezing_theorem type Message106598915.
- Non-squeezing_theorem type Proposition106750804.
- Non-squeezing_theorem type Statement106722453.
- Non-squeezing_theorem type Theorem106752293.
- Non-squeezing_theorem type TheoremsInGeometry.
- Non-squeezing_theorem comment "The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven in 1985 by the winner of the 2009 Abel Prize, Mikhail Gromov. The theorem states that one cannot embed a sphere into a cylinder via a symplectic map unless the radius of the sphere is less than or equal to the radius of the cylinder.".
- Non-squeezing_theorem label "Non-squeezing theorem".
- Non-squeezing_theorem label "Théorème de non-plongement de Gromov".
- Non-squeezing_theorem sameAs Théorème_de_non-plongement_de_Gromov.
- Non-squeezing_theorem sameAs m.06_w6_v.
- Non-squeezing_theorem sameAs Q3527214.
- Non-squeezing_theorem sameAs Q3527214.
- Non-squeezing_theorem sameAs Non-squeezing_theorem.
- Non-squeezing_theorem wasDerivedFrom Non-squeezing_theorem?oldid=598212275.
- Non-squeezing_theorem isPrimaryTopicOf Non-squeezing_theorem.