Journal of Differential Geometry

The Hofer Conjecture on Embedding Symplectic Ellipsoids

Dusa McDuff

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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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J. Differential Geom., Volume 88, Number 3 (2011), 519-532.

First available in Project Euclid: 15 November 2011

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McDuff, Dusa. The Hofer Conjecture on Embedding Symplectic Ellipsoids. J. Differential Geom. 88 (2011), no. 3, 519--532. doi:10.4310/jdg/1321366358.

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