We give in a real analytic almost complex structure , a real analytic hypersurface and a vector in the Levi null set at of , such that there is no germ of -holomorphic disc included in with and , although the Levi form of has constant rank. Then for any hypersurface and any complex structure , we give sufficient conditions under which there exists such a germ of disc.
Nous définissons dans une structure presque complexe réelle analytique , une hypersurface réelle analytique dont la forme de Levi est de rang constant et un vecteur appartenant au noyau de la forme de Levi de en tels qu’il n’existe pas de germe de disque -holomorphe inclus dans vérifiant et . Nous donnons ensuite des conditions suffisantes pour qu’un tel germe de disque existe.
Keywords: almost complex structure, $J$-holomorphic disc, hypersurface
Mot clés : Structure presque complexe, disque $J$-holomorphe, hypersurface
@article{AIF_2014__64_5_2223_0, author = {Alexandre, William and Mazzilli, Emmanuel}, title = {$J$-holomorphic discs and real analytic hypersurfaces}, journal = {Annales de l'Institut Fourier}, pages = {2223--2250}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {5}, year = {2014}, doi = {10.5802/aif.2910}, zbl = {06387337}, mrnumber = {3330937}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2910/} }
TY - JOUR AU - Alexandre, William AU - Mazzilli, Emmanuel TI - $J$-holomorphic discs and real analytic hypersurfaces JO - Annales de l'Institut Fourier PY - 2014 SP - 2223 EP - 2250 VL - 64 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2910/ DO - 10.5802/aif.2910 LA - en ID - AIF_2014__64_5_2223_0 ER -
%0 Journal Article %A Alexandre, William %A Mazzilli, Emmanuel %T $J$-holomorphic discs and real analytic hypersurfaces %J Annales de l'Institut Fourier %D 2014 %P 2223-2250 %V 64 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2910/ %R 10.5802/aif.2910 %G en %F AIF_2014__64_5_2223_0
Alexandre, William; Mazzilli, Emmanuel. $J$-holomorphic discs and real analytic hypersurfaces. Annales de l'Institut Fourier, Volume 64 (2014) no. 5, pp. 2223-2250. doi : 10.5802/aif.2910. http://www.numdam.org/articles/10.5802/aif.2910/
[1] Regular type of real hyper-surface in (almost) complex manifolds, Math. Z., Volume 248 (2004), pp. 757-772 | DOI | MR | Zbl
[2] Local Complex foliation of Real Submanifolds, Math. Ann., Volume 209 (1974), pp. 1-30 | DOI | MR | Zbl
[3] Schwarz-type lemmas for solutions of -inequalities and complete hyperbolicity of almost complex manifolds, Ann. Inst. Fourier (Grenoble), Volume 54 (2004) no. 7, pp. 2387-2435 (2005) | DOI | Numdam | MR | Zbl
[4] Schwarz reflection principle, boundary regularity and compactness for -complex curves, Ann. Inst. Fourier (Grenoble), Volume 60 (2010) no. 4, pp. 1489-1513 | DOI | Numdam | MR | Zbl
[5] Pseudoholomorphic discs attached to CR-submanifolds of almost complex spaces, Bull. Sci. Math., Volume 129 (2005) no. 5, pp. 398-414 | DOI | MR | Zbl
[6] An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953 | MR | Zbl
[7] Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan, Volume 18 (1966), pp. 398-404 | DOI | MR | Zbl
[8] Some properties of holomorphic curves in almost complex manifolds, Holomorphic curves in symplectic geometry (Prog. Math.), Volume 117, Birkhauser, Basel, 1994, pp. 165-189 | MR
Cited by Sources: