Involve: A Journal of Mathematics
- Volume 10, Number 2 (2017), 219-242.
Symplectic embeddings of four-dimensional ellipsoids into polydiscs
McDuff and Schlenk recently determined exactly when a four-dimensional symplectic ellipsoid symplectically embeds into a symplectic ball. Similarly, Frenkel and Müller recently determined exactly when a symplectic ellipsoid symplectically embeds into a symplectic cube. Symplectic embeddings of more complicated sets, however, remain mostly unexplored. We study when a symplectic ellipsoid symplectically embeds into a polydisc . We prove that there exists a constant depending only on (here, is assumed greater than ) such that if is greater than , then the only obstruction to symplectically embedding into is the volume obstruction. We also conjecture exactly when an ellipsoid embeds into a scaling of for , and conjecture about the set of such that the only obstruction to embedding into a scaling of is the volume. Finally, we verify our conjecture for .
Involve, Volume 10, Number 2 (2017), 219-242.
Received: 8 September 2014
Revised: 21 June 2015
Accepted: 1 July 2015
First available in Project Euclid: 13 December 2017
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Burkhart, Madeleine; Panescu, Priera; Timmons, Max. Symplectic embeddings of four-dimensional ellipsoids into polydiscs. Involve 10 (2017), no. 2, 219--242. doi:10.2140/involve.2017.10.219. https://projecteuclid.org/euclid.involve/1513135628