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Symplectic embeddings of polydisks. (English) Zbl 1153.53060

Summary: If \(P\) and \(P^{'}\) are symplectic polydisks of radii \(R_{1}\leq \cdots\leq R_{n}\) and \(R_{1}^{'}\leq \cdots\leq R_{n}^{'}\), respectively, then we prove that \(P\) symplectically embeds in \(P^{'}\) provided that \(C(n) R_{1}\leq R_{1}^{'}\) and \(C (n) R_{1}\dots R_{n}\leq R_{1}^{'}\dots R_{n}^{'}\). Up to a constant factor, these conditions are optimal.

MSC:

53D35 Global theory of symplectic and contact manifolds
53D05 Symplectic manifolds (general theory)
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References:

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