We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.
@article{ASNSP_2007_5_6_4_661_0, author = {Brunella, Marco}, title = {Singular {Levi-flat} hypersurfaces and codimension one foliations}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {661--672}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 6}, number = {4}, year = {2007}, mrnumber = {2394414}, zbl = {1214.32012}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2007_5_6_4_661_0/} }
TY - JOUR AU - Brunella, Marco TI - Singular Levi-flat hypersurfaces and codimension one foliations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 661 EP - 672 VL - 6 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2007_5_6_4_661_0/ LA - en ID - ASNSP_2007_5_6_4_661_0 ER -
%0 Journal Article %A Brunella, Marco %T Singular Levi-flat hypersurfaces and codimension one foliations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 661-672 %V 6 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2007_5_6_4_661_0/ %G en %F ASNSP_2007_5_6_4_661_0
Brunella, Marco. Singular Levi-flat hypersurfaces and codimension one foliations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 4, pp. 661-672. http://www.numdam.org/item/ASNSP_2007_5_6_4_661_0/
[1] “Real Submanifolds in Complex Space and their Mappings”, Princeton Mathematical Series 47, 1999. | MR | Zbl
, and ,[2] Singular Levi-flat real analytic hypersurfaces, Amer. J. Math. 121 (1999), 23-53. | MR | Zbl
and ,[3] Reduction of the singularities of codimension one singular foliations in dimension three, Ann. of Math. 160 (2004), 907-1011. | MR | Zbl
,[4] Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957), 77-99. | EuDML | Numdam | MR | Zbl
,[5] Feuilletages holomorphes de codimension 1. Réduction des singularités en petites dimensions et applications, Panor. Synthèses 8 (1999), 11-47. | MR | Zbl
,[6] Pseudoconvex domains with real-analytic boundary, Ann. of Math. 107 (1978), 371-384. | MR | Zbl
and ,[7] “Introduction to Complex Analytic Geometry”, Birkhäuser, 1991. | MR | Zbl
,