Journal of Differential Geometry

Symplectic embeddings from concave toric domains into convex ones

Dan Cristofaro-Gardiner

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Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. In “Symplectic embeddings into four-dimensional concave toric domains”, the author, Choi, Frenkel, Hutchings and Ramos computed the ECH capacities of all “concave toric domains”, and showed that these give sharp obstructions in several interesting cases. We show that these obstructions are sharp for all symplectic embeddings of concave toric domains into “convex” ones. In an appendix with Choi, we prove a new formula for the ECH capacities of convex toric domains, which shows that they are determined by the ECH capacities of a corresponding collection of balls.

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J. Differential Geom., Volume 112, Number 2 (2019), 199-232.

Received: 25 January 2015
First available in Project Euclid: 6 June 2019

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Cristofaro-Gardiner, Dan. Symplectic embeddings from concave toric domains into convex ones. J. Differential Geom. 112 (2019), no. 2, 199--232. doi:10.4310/jdg/1559786421.

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