Illinois Journal of Mathematics

Hartogs figure and symplectic non-squeezing

Alexandre Sukhov and Alexander Tumanov

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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.

Article information

Illinois J. Math., Volume 56, Number 1 (2012), 221-233.

First available in Project Euclid: 27 September 2013

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Zentralblatt MATH identifier

Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)


Sukhov, Alexandre; Tumanov, Alexander. Hartogs figure and symplectic non-squeezing. Illinois J. Math. 56 (2012), no. 1, 221--233. doi:10.1215/ijm/1380287469.

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