Pseudoholomorphic discs and symplectic structures in Hilbert space

2014/11/14 by Sukhov, Alexandre, Tumanov, Alexander
#32H02 #53C15 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1411.3993

Abstract

We develop the theory of J-holomorphic discs in Hilbert spaces with almost complex structures. As an aplication, we prove a version of Gromov's symplectic non-squeezing theorem for Hilbert spaces. It can be applied to short-time symplectic flows of a wide class of Hamiltonian PDEs.

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