Symplectic embeddings and the lagrangian bidisk

2015/09/30 by Vinicius Gripp Barros Ramos · 1 citation
Mathematics · #math.SG

paper · pdf · doi:10.1215/00127094-0000011x

published as Duke Math. J. 166, no. 9 (2017), 1703-1738 · 31 pages, 4 figures; minor changes to presentation, updated references. To appear in Duke Mathematical Journal

arxiv created 2016/11/14 · arxiv updated 2017/10/18

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.

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