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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.
Barrett, D. E., and Fornaess, John Erik. "On the smoothness of Levi-foliations.." Publicacions Matemàtiques 32.2 (1988): 171-177. <http://eudml.org/doc/41049>.
@article{Barrett1988, abstract = {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.}, author = {Barrett, D. E., Fornaess, John Erik}, journal = {Publicacions Matemàtiques}, keywords = {Foliaciones; Hipersuperficies; Regularidad; Levi flat; foliation}, language = {eng}, number = {2}, pages = {171-177}, title = {On the smoothness of Levi-foliations.}, url = {http://eudml.org/doc/41049}, volume = {32}, year = {1988}, }
TY - JOUR AU - Barrett, D. E. AU - Fornaess, John Erik TI - On the smoothness of Levi-foliations. JO - Publicacions Matemàtiques PY - 1988 VL - 32 IS - 2 SP - 171 EP - 177 AB - 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. LA - eng KW - Foliaciones; Hipersuperficies; Regularidad; Levi flat; foliation UR - http://eudml.org/doc/41049 ER -