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Symplectic embeddings of ellipsoids in dimension greater than four

Olguta Buse and Richard Hind

Geometry & Topology 15 (2011) 2091–2110

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(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.

symplectic embedding, packing stability
Mathematical Subject Classification 2010
Primary: 53D35, 57R17
Received: 18 April 2011
Revised: 16 August 2011
Accepted: 13 September 2011
Published: 28 October 2011
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Ronald Fintushel
Olguta Buse
Department of Mathematics
Indiana University Purdue University Indianapolis
Indianapolis IN 46202
Richard Hind
Department of Mathematics
University of Notre Dame
Notre Dame IN 46556