Symplectic embeddings of ellipsoids in dimension greater than four

Buse, Olguta¹ ; Hind, Richard²

¹ Department of Mathematics, Indiana University Purdue University Indianapolis, Indianapolis IN 46202, USA
² Department of Mathematics, University of Notre Dame, Notre Dame IN 46556, USA

Geometry & topology, Tome 15 (2011) no. 4, pp. 2091-2110.

Résumé

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 $4$.

Détail

DOI : 10.2140/gt.2011.15.2091

Classification : 53D35, 57R17
Keywords: symplectic embedding, packing stability

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