Let be a manifold with an almost complex structure tamed by a symplectic form . We suppose that 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 can be foliated by the boundaries of pseudoholomorphic discs.
Soit une variété dont la structure presque complexe est contrôlée par la forme symplectique . On suppose de dimension complexe deux, Levi-convexe et à géométrie bornée. On démontre que toute 2-sphère possédant deux points elliptiques et plongée dans le bord de est feuilletée par des bords de disques pseudoholomorphes.
@article{AFST_2011_6_20_3_515_0, author = {Gaussier, Herv\'e and Sukhov, Alexandre}, title = {Levi-flat filling of real two-spheres in symplectic manifolds {(I)}}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {515--539}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 20}, number = {3}, year = {2011}, doi = {10.5802/afst.1316}, zbl = {1242.53107}, mrnumber = {2894837}, language = {en}, url = {http://www.numdam.org/articles/10.5802/afst.1316/} }
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 PY - 2011 SP - 515 EP - 539 VL - 20 IS - 3 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1316/ DO - 10.5802/afst.1316 LA - en ID - AFST_2011_6_20_3_515_0 ER -
%0 Journal Article %A Gaussier, Hervé %A Sukhov, Alexandre %T Levi-flat filling of real two-spheres in symplectic manifolds (I) %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 515-539 %V 20 %N 3 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1316/ %R 10.5802/afst.1316 %G en %F AFST_2011_6_20_3_515_0
Gaussier, Hervé; Sukhov, Alexandre. Levi-flat filling of real two-spheres in symplectic manifolds (I). Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 3, pp. 515-539. doi : 10.5802/afst.1316. http://www.numdam.org/articles/10.5802/afst.1316/
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