We study the regularity of the induced foliation of a Levi-flat hypersurface in Cn, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.
@article{urn:eudml:doc:41049,
title = {On the smoothness of Levi-foliations.},
journal = {Publicacions Matem\`atiques},
volume = {32},
year = {1988},
pages = {171-177},
zbl = {0663.32014},
mrnumber = {MR0975896},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41049}
}
Barrett, D. E.; Fornaess, John Erik. On the smoothness of Levi-foliations.. Publicacions Matemàtiques, Tome 32 (1988) pp. 171-177. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41049/