# $J$-holomorphic discs and real analytic hypersurfaces

William Alexandre^{[1]}; Emmanuel Mazzilli^{[1]}

- [1] 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.

Annales de l’institut Fourier (2014)

- Volume: 64, Issue: 5, page 2223-2250
- ISSN: 0373-0956

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topAlexandre, William, and Mazzilli, Emmanuel. "$J$-holomorphic discs and real analytic hypersurfaces." Annales de l’institut Fourier 64.5 (2014): 2223-2250. <http://eudml.org/doc/275494>.

@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 -

## References

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