J-holomorphic discs and real analytic hypersurfaces
Complex Variables
2012-11-19 v2
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 f included in M with f(0)=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.
Keywords
Cite
@article{arxiv.1211.3620,
title = {J-holomorphic discs and real analytic hypersurfaces},
author = {William Alexandre and Emmanuel Mazzilli},
journal= {arXiv preprint arXiv:1211.3620},
year = {2012}
}