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Journal of Topology Advance Access originally published online on February 25, 2009
Journal of Topology 2009 2(1):1-22; doi:10.1112/jtopol/jtn031
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© 2009 London Mathematical Society

Symplectic embeddings of 4-dimensional ellipsoids

Dusa McDuff

Department of Mathematics, Barnard College, Columbia University, New York, NY 10027-6598, USA, dusa@math.columbia.edu


  Abstract

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 CP2. 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 CP2, 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 >= 9, thus answering a question raised by Hofer.

Received March 31, 2008.

2000 Mathematics Subject Classification 53D05


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