If there is a symplectic embeddingthen . Symplectic volume alone does not imply this radius obstruction.
The symplectic manifold contains symplectic balls of arbitrarily large radius. A steep linear Lagrangian graph in has a thin neighborhood that injects under the quotient , while a symplectic base-fiber dilation fits a large round ball into that long thin neighborhood.
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The Non-Squeezing Theorem is a fundamental result in symplectic geometry, a branch of mathematics that studies structures and properties of spaces that are equipped with a symplectic form. Specifically, the theorem addresses the concept of symplectic embeddings, which are mappings between symplectic manifolds that preserve the symplectic structure. The Non-Squeezing Theorem asserts that there are limitations on how one can "squeeze" or transform symplectic spaces.