Symplectic embeddings of ellipsoids in dimension greater than four

We study symplectic embeddings of ellipsoids into balls. In the main construction, we show that a given embedding of 2 m-dimensional ellipsoids can be suspended to embeddings of ellipsoids in any higher dimension. In dimension 6, 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.