Symplectic embeddings of 4-dimensional ellipsoids
| dc.creator | McDuff, Dusa | |
| dc.date | 2008-01-30 | |
| dc.date | 2008-12-02 | |
| dc.date.accessioned | 2026-07-07T12:07:58Z | |
| dc.date.available | 2026-07-07T12:07:58Z | |
| dc.description | We show how to reduce the problem of symplectically embedding one 4-dimensional rational ellipsoid into another to a problem of embedding disjoint unions of balls into appropriate blow ups of \C P^2. For example, the problem of embedding the ellipsoid E(1,k) into a ball B is equivalent to that of embedding k disjoint equal balls into \C P^2, and so can be solved by the work of Gromov, McDuff--Polterovich and Biran. (Here k is the ratio of the area of the major axis to that of the minor axis.) As a consequence we show that the ball may be fully filled by the ellipsoid E(1,k) for k=1,4 and all k\ge 9, thus answering a question raised by Hofer. | |
| dc.description | 24 pages, 9 figures; some proofs clarified, relation to continued fractions explained. v3: references added, to appear in Journal of Topology | |
| dc.identifier | https://arxiv.org/abs/0801.4665 | |
| dc.identifier | http://arxiv.org/abs/0801.4665 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209161 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D05 | |
| dc.title | Symplectic embeddings of 4-dimensional ellipsoids | |
| dc.type | text |