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Symplectic
embeddings of four-dimensional ellipsoids into polydiscs
Madeleine Burkhart, Priera Panescu and Max Timmons
Vol. 10 (2017), No. 2, 219–242
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Abstract |
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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 . |
Keywords
symplectic geometry
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Mathematical Subject Classification 2010
Primary: 53DXX
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Milestones
Received: 8 September 2014
Revised: 21 June 2015
Accepted: 1 July 2015
Published: 10 November 2016
Communicated by Bjorn Poonen
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Authors |
| Madeleine Burkhart | |
| Mathematics Department University of Washington Padelford Hall C-110 Seattle, WA 98195 United States |
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| Priera Panescu | |
| University of California Santa Cruz, CA 95064 United States |
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| Max Timmons | |
| Massachusetts Institute of
Technology 450 Memorial Drive Cambridge, MA 02139 United States |
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