#### Volume 15, issue 4 (2011)

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Symplectic embeddings of ellipsoids in dimension greater than four

### Olguta Buse and Richard Hind

Geometry & Topology 15 (2011) 2091–2110
##### 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 $6$, 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 $E\left(1,\dots ,a\right)$. 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 $4$.

##### Keywords
symplectic embedding, packing stability
##### Mathematical Subject Classification 2010
Primary: 53D35, 57R17
##### Publication
Revised: 16 August 2011
Accepted: 13 September 2011
Published: 28 October 2011
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Ronald Fintushel
##### Authors
 Olguta Buse Department of Mathematics Indiana University Purdue University Indianapolis Indianapolis IN 46202 USA Richard Hind Department of Mathematics University of Notre Dame Notre Dame IN 46556 USA