Symplectic embeddings of ellipsoids in dimension greater than four

Buse, Olguta; Hind, Richard

doi:10.2140/gt.2011.15.2091

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Symplectic embeddings of ellipsoids in dimension greater than four

Olguta Buse and Richard Hind

Geometry & Topology 15 (2011) 2091–2110

DOI: 10.2140/gt.2011.15.2091

Abstract

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 $E (1, \dots, a)$ . 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 $4$ .

Keywords

symplectic embedding, packing stability

Mathematical Subject Classification 2010

Primary: 53D35, 57R17

References

Publication

Received: 18 April 2011

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

Volume 15, issue 4 (2011)