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2017 Symplectic embeddings of four-dimensional ellipsoids into polydiscs
Madeleine Burkhart, Priera Panescu, Max Timmons
Involve 10(2): 219-242 (2017). DOI: 10.2140/involve.2017.10.219

Abstract

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 E(a,b) symplectically embeds into a polydisc P(c,d). We prove that there exists a constant C depending only on dc (here, d is assumed greater than c) such that if ba is greater than C, then the only obstruction to symplectically embedding E(a,b) into P(c,d) is the volume obstruction. We also conjecture exactly when an ellipsoid embeds into a scaling of P(1,b) for b 6, and conjecture about the set of (a,b) such that the only obstruction to embedding E(1,a) into a scaling of P(1,b) is the volume. Finally, we verify our conjecture for b = 13 2 .

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Madeleine Burkhart. Priera Panescu. Max Timmons. "Symplectic embeddings of four-dimensional ellipsoids into polydiscs." Involve 10 (2) 219 - 242, 2017. https://doi.org/10.2140/involve.2017.10.219

Information

Received: 8 September 2014; Revised: 21 June 2015; Accepted: 1 July 2015; Published: 2017
First available in Project Euclid: 13 December 2017

zbMATH: 1353.53084
MathSciNet: MR3574298
Digital Object Identifier: 10.2140/involve.2017.10.219

Subjects:
Primary: 53Dxx

Keywords: symplectic geometry

Rights: Copyright © 2017 Mathematical Sciences Publishers

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