Symplectic embeddings and the lagrangian bidisk

@article{Ramos2017SymplecticEA,
  title={Symplectic embeddings and the lagrangian bidisk},
  author={Vinicius G. B. Ramos},
  journal={Duke Mathematical Journal},
  year={2017},
  volume={166},
  pages={1703-1738}
}
In this paper we obtain sharp obstructions to the symplectic embedding of the lagrangian bidisk into four-dimensional balls, ellipsoids and symplectic polydisks. We prove, in fact, that the interior of the lagrangian bidisk is symplectomorphic to a concave toric domain using ideas that come from billiards on a round disk. In particular, we answer a question of Ostrover. We also obtain sharp obstructions to some embeddings of ellipsoids into the lagrangian bidisk. 
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