# J-holomorphic discs and real analytic hypersurfaces

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 f included in M with f0=0 and \frac{\partial f}{\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 necessary conditions under which there exists such a germ of disc.

Author: William Alexandre; Emmanuel Mazzilli

Source: https://archive.org/