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.
"Hartogs figure and symplectic non-squeezing." Illinois J. Math. 56 (1) 221 - 233, Spring 2012. https://doi.org/10.1215/ijm/1380287469