Gromov's Non-Squeezing Theorem states that a ball in symplectic space cannot be mapped, by a transformation preserving the symplectic structure, into a cylinder of smaller radius, even though such a map is easy to achieve using an ordinary volume-preserving transformation. Named for Mikhail Gromov, who proved it in 1985, it revealed that symplectic geometry carries a genuine rigidity invisible to volume alone, and it launched the modern theory of symplectic capacities.
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StatementOne 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 cylinder. 1 Classification
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Source Non-squeezing theorem (Wikipedia)
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Source Gromov's non-squeezing theorem (Wikipedia)
Additional Source Non-squeezing theorem (Wikipedia)Lead
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1. Gromov's non-squeezing theorem (Wikipedia)
Background and statement section
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 cylinder.
Background and statement section, second sentence
It was first proven in 1985 by Mikhail Gromov.
Proved By: Mikhail Gromov, Lead section
It was first proven in 1985 by Mikhail Gromov.
In Group: Geometric and Differential Topology, Lead section
The non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry.
View the SourceNon-squeezing theorem (Wikipedia)
In Branch: Geometry, Lead sentence
one of the most important theorems in symplectic geometry.
Proved By: Mikhail Gromov, Lead
It was first proven in 1985 by Mikhail Gromov.
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