Symplectic embeddings of 4-dimensional ellipsoids |
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Authors: | McDuff Dusa |
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Institution: | Department of Mathematics, Barnard College, Columbia University, New York, NY 10027-6598, USA, dusa@math.columbia.edu |
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Abstract: | We show how to reduce the problem of symplectically embeddingone 4-dimensional rational ellipsoid into another to a problemof embedding disjoint unions of balls into P2. For example,the problem of embedding the ellipsoid E(1, k) into a ball Bis equivalent to that of embedding k disjoint equal balls into P2, 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 axisto that of the minor axis.) As a consequence we show that theball 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. |
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