$J$-holomorphic discs and real analytic hypersurfaces

@article{Alexandre2014,
abstract = {We give in $\mathbb\{R\}^6$ a real analytic almost complex structure $J$, a real analytic hypersurface $M$ and a vector $v$ in the Levi null set at $0$ of $M$, such that there is no germ of $J$-holomorphic disc $\gamma $ included in $M$ with $\gamma (0)=0$ and $\frac\{\partial \gamma \}\{\partial x\}(0)=v$, although the Levi form of $M$ has constant rank. Then for any hypersurface $M$ and any complex structure $J$, we give sufficient conditions under which there exists such a germ of disc.},
affiliation = {Laboratoire Paul Painlevé U.M.R. CNRS 8524 U.F.R. de Mathématiques cité scientifique Université Lille 1 F59 655 Villeneuve d’Ascq Cedex, France.; Laboratoire Paul Painlevé U.M.R. CNRS 8524 U.F.R. de Mathématiques cité scientifique Université Lille 1 F59 655 Villeneuve d’Ascq Cedex, France.},
author = {Alexandre, William, Mazzilli, Emmanuel},
journal = {Annales de l’institut Fourier},
keywords = {almost complex structure; $J$-holomorphic disc; hypersurface; -holomorphic disc; Levi form},
language = {eng},
number = {5},
pages = {2223-2250},
publisher = {Association des Annales de l’institut Fourier},
title = {$J$-holomorphic discs and real analytic hypersurfaces},
url = {http://eudml.org/doc/275494},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Alexandre, William
AU - Mazzilli, Emmanuel
TI - $J$-holomorphic discs and real analytic hypersurfaces
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 5
SP - 2223
EP - 2250
AB - We give in $\mathbb{R}^6$ a real analytic almost complex structure $J$, a real analytic hypersurface $M$ and a vector $v$ in the Levi null set at $0$ of $M$, such that there is no germ of $J$-holomorphic disc $\gamma $ included in $M$ with $\gamma (0)=0$ and $\frac{\partial \gamma }{\partial x}(0)=v$, although the Levi form of $M$ has constant rank. Then for any hypersurface $M$ and any complex structure $J$, we give sufficient conditions under which there exists such a germ of disc.
LA - eng
KW - almost complex structure; $J$-holomorphic disc; hypersurface; -holomorphic disc; Levi form
UR - http://eudml.org/doc/275494
ER -