Journal of Differential Geometry

The Hofer Conjecture on Embedding Symplectic Ellipsoids

Dusa McDuff

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 15 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1321366358

Digital Object Identifier
doi:10.4310/jdg/1321366358

Mathematical Reviews number (MathSciNet)
MR2844441

Zentralblatt MATH identifier
1239.53109

Citation

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


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