Illinois Journal of Mathematics

Hartogs figure and symplectic non-squeezing

Alexandre Sukhov and Alexander Tumanov

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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.

Article information

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

Dates
First available in Project Euclid: 27 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1380287469

Digital Object Identifier
doi:10.1215/ijm/1380287469

Mathematical Reviews number (MathSciNet)
MR2892615

Zentralblatt MATH identifier
1284.32016

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

Citation

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


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