Levi-flat filling of real two-spheres in symplectic manifolds (I)

Hervé Gaussier[1]; Alexandre Sukhov[2]

  • [1] Université Joseph Fourier, 100 rue des Maths, 38402 Saint Martin d’Hères, France
  • [2] Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé, U.F.R. de Mathématique, 59655 Villeneuve d’Ascq, Cedex, France

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 3, page 515-539
  • ISSN: 0240-2963

Abstract

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Let ( M , J , ω ) be a manifold with an almost complex structure J tamed by a symplectic form ω . We suppose that M has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of M can be foliated by the boundaries of pseudoholomorphic discs.

How to cite

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Gaussier, Hervé, and Sukhov, Alexandre. "Levi-flat filling of real two-spheres in symplectic manifolds (I)." Annales de la faculté des sciences de Toulouse Mathématiques 20.3 (2011): 515-539. <http://eudml.org/doc/219817>.

@article{Gaussier2011,
abstract = {Let $(M,J,\omega )$ be a manifold with an almost complex structure $J$ tamed by a symplectic form $\omega $. We suppose that $M$ has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of $M$ can be foliated by the boundaries of pseudoholomorphic discs.},
affiliation = {Université Joseph Fourier, 100 rue des Maths, 38402 Saint Martin d’Hères, France; Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé, U.F.R. de Mathématique, 59655 Villeneuve d’Ascq, Cedex, France},
author = {Gaussier, Hervé, Sukhov, Alexandre},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Bishop disks; confoliations; Levi-flat hypersurfaces; elliptic points},
language = {eng},
month = {7},
number = {3},
pages = {515-539},
publisher = {Université Paul Sabatier, Toulouse},
title = {Levi-flat filling of real two-spheres in symplectic manifolds (I)},
url = {http://eudml.org/doc/219817},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Gaussier, Hervé
AU - Sukhov, Alexandre
TI - Levi-flat filling of real two-spheres in symplectic manifolds (I)
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/7//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 3
SP - 515
EP - 539
AB - Let $(M,J,\omega )$ be a manifold with an almost complex structure $J$ tamed by a symplectic form $\omega $. We suppose that $M$ has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of $M$ can be foliated by the boundaries of pseudoholomorphic discs.
LA - eng
KW - Bishop disks; confoliations; Levi-flat hypersurfaces; elliptic points
UR - http://eudml.org/doc/219817
ER -

References

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