On symplectic folding
نویسنده
چکیده
We study the rigidity and flexibility of symplectic embeddings of simple shapes. It is first proved that under the condition r n ≤ 2r 1 the symplectic ellipsoid E(r1, . . . , rn) with radii r1 ≤ · · · ≤ rn does not embed in a ball of radius strictly smaller than rn. We then use symplectic folding to see that this condition is sharp and to construct some nearly optimal embeddings of ellipsoids and polydiscs into balls and cubes. It is finally shown that any connected symplectic manifold of finite volume may be asymptotically filled with skinny ellipsoids or polydiscs.
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