Symplectic embeddings of 4-dimensional ellipsoids

Details Symplectic embeddings of 4-dimensional ellipsoids Symplectic embeddings of 4-dimensional ellipsoids

2008-01-30

arxiv.org/abs/0801.4665v3

Mathematics

Symplectic Geometry

24 pages, 9 figures; some proofs clarified, relation to continued fractions explained. v3: references added, to appear in Jour

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Symplectic embeddings of 4-dimensional ellipsoids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Symplectic embeddings of 4-dimensional ellipsoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic embeddings of 4-dimensional ellipsoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-121775