no. 4
Singular Levi-flat hypersurfaces and codimension one foliations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 661-672

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.

Classification : 32V25, 32S65, 32C05 
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     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},
     year = {2007},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {4},
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     zbl = {1214.32012},
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Brunella, Marco. Singular Levi-flat hypersurfaces and codimension one foliations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 661-672. https://www.numdam.org/item/ASNSP_2007_5_6_4_661_0/

[1] M. S. Baouendi, P. Ebenfelt and L. P. Rothschild, “Real Submanifolds in Complex Space and their Mappings”, Princeton Mathematical Series 47, 1999. | Zbl | MR

[2] D. Burns and X. Gong, Singular Levi-flat real analytic hypersurfaces, Amer. J. Math. 121 (1999), 23-53. | Zbl | MR

[3] F. Cano, Reduction of the singularities of codimension one singular foliations in dimension three, Ann. of Math. 160 (2004), 907-1011. | Zbl | MR

[4] H. Cartan, Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957), 77-99. | Zbl | MR | Numdam | EuDML

[5] D. Cerveau, Feuilletages holomorphes de codimension 1. Réduction des singularités en petites dimensions et applications, Panor. Synthèses 8 (1999), 11-47. | Zbl | MR

[6] K. Diederich and J. E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math. 107 (1978), 371-384. | Zbl | MR

[7] S. Lojasiewicz, “Introduction to Complex Analytic Geometry”, Birkhäuser, 1991. | Zbl | MR