On Orthogonal Projections of Symplectic balls

Abstract

We study the orthogonal projections of symplectic balls in ${\mathbb{R}}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a refinement of a recent very interesting result of Abbondandolo and Matveyev extending the linear version of Gromov's non-squeezing theorem. We use a conceptually simpler approach where the Schur complement of a matrix plays a central role.

10 pages

References in corpus (2)

• Sharp systolic inequalities for Reeb flows on the three-sphere
• Symplectic embeddings of polydisks