Symplectic embeddings of ellipsoids in dimension greater than four

Abstract

We study symplectic embeddings of ellipsoids into balls. In the main construction, we show that a given embedding of 2m-dimensional ellipsoids can be suspended to embeddings of ellipsoids in any higher dimension. In dimension 6,s if the ratio of the areas of any two axes is sufficiently large then the ellipsoid is flexible in the sense that it fully fills a ball. We also show that the same property holds in all dimensions for sufficiently thin ellipsoids E(1,..., a). A consequence of our study is that in arbitrary dimension a ball can be fully filled by any sufficiently large number of identical smaller balls, thus generalizing a result of Biran valid in dimension 4.

20 pages, 3 figures

References in corpus (2)

• Symplectic embeddings of 4-dimensional ellipsoids: erratum
• Some 6-dimensional Hamiltonian S^1 manifolds

Cited by in corpus (10)

• Some optimal embeddings of symplectic ellipsoids
• Symplectic embeddings of four-dimensional ellipsoids into integral polydiscs
• Ellipsoid embeddings and symplectic packing stability
• Nongeneric J-holomorphic curves and singular inflation
• Bounding Lagrangian widths via geodesic paths
• Irreversibility from staircases in symplectic embeddings
• Topology of symplectomorphism groups and ball-swappings
• Symplectic isotopy classes of ellipsoids and polydisks in dimension greater than four
• Quantitative Results on Symplectic Barriers
• Packing stability for symplectic $4$-manifolds