The hofer conjecture on embedding symplectic ellipsoids

Dusa McDuff Columbia University

Differential Geometry mathscidoc:1609.10231

Journal of Differential Geometry, 88, (3), 519-532, 2011
In this note we show that one open 4-dimensional ellipsoid embeds symplectically into another if and only if the ECH capacities of the first are no larger than those of the second. This proves a conjecture due to Hofer. The argument uses the equivalence of the ellipsoidal embedding problem with a ball embedding problem that was recently established by McDuff. Its method is inspired by Hutchings’ recent results on embedded contact homology (ECH) capacities but does not use them.
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@inproceedings{dusa2011the,
  title={THE HOFER CONJECTURE ON EMBEDDING SYMPLECTIC ELLIPSOIDS},
  author={Dusa McDuff},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205103965624892},
  booktitle={Journal of Differential Geometry},
  volume={88},
  number={3},
  pages={519-532},
  year={2011},
}
Dusa McDuff. THE HOFER CONJECTURE ON EMBEDDING SYMPLECTIC ELLIPSOIDS. 2011. Vol. 88. In Journal of Differential Geometry. pp.519-532. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205103965624892.
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