Hartogs figure and symplectic non-squeezing

Abstract

We solve a problem on filling by Levi-flat hypersurfaces for a class of totally real 2-tori in a real 4-manifold with an almost complex structure tamed by an exact symplectic form. As an application we obtain a simple proof of Gromov's non-squeezing theorem in dimension 4 and new results on rigidity of symplectic structures.

In this version, we've made minor improvements and corrected typos; 12 pages