Symplectic embeddings and the lagrangian bidisk

Abstract

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.

31 pages, 4 figures; minor changes to presentation, updated references. To appear in Duke Mathematical Journal

References in corpus (4)

• Symplectic embeddings of 4-dimensional ellipsoids: erratum
• Symplectic embeddings into four-dimensional concave toric domains
• When symplectic topology meets Banach space geometry
• On symplectic capacities of toric domains

Cited by in corpus (8)

• Symplectic embeddings into disk cotangent bundles
• Symplectic capacities of disc cotangent bundles of flat tori
• On the Ekeland-Hofer symplectic capacities of the real bidisc
• Riemannian distance and symplectic embeddings in cotangent bundle
• The Viterbo's capacity conjectures for convex toric domains and the product of a $1$-unconditional convex body and its polar
• On symplectic capacities and their blind spots
• Higher $P$-symmetric Ekeland-Hofer capacities
• From Lagrangian Products to Toric Domains via the Toda Lattice