Singular Levi-flat hypersurfaces and codimension one foliations

Marco Brunella

Type: Article

Publication Date: 2009-12-02

Citations: 24

DOI: https://doi.org/10.2422/2036-2145.2007.4.07

Abstract

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.

Locations

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE - View - PDF
French digital mathematics library (Numdam) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Singular Levi-flat hypersurfaces and codimension one foliations	2007	Marco Brunella
+	Local Levi-flat hypersurfaces invariants by a codimension one holomorphic foliation	2011	Dominique Cerveau Alcides Lins Neto
+ PDF Chat	Pull-back of singular Levi-flat hypersurfaces	2021	Andrés Beltrán Arturo Fernández‐Pérez Hernán Neciosup
+	Pull-back of singular Levi-flat hypersurfaces	2021	Andrés Beltrán Arturo Fernández‐Pérez Hernán Neciosup
+	Pull-back of singular Levi-flat hypersurfaces	2021	Andrès Blanco Beltràn Arturo Fernández-Pérez Hernán Neciosup
+	Singular Levi-flat real analytic hypersurfaces	1999	D. Burns Xianghong Gong
+	Germs of singular Levi-flat hypersurfaces and holomorphic foliations	2014	Rasul Shafikov Alexandre Sukhov
+	Germs of singular Levi-flat hypersurfaces and holomorphic foliations	2014	Rasul Shafikov Alexandre Sukhov
+ PDF Chat	Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations	2017	Andrés Beltrán Arturo Fernández‐Pérez Hernán Neciosup
+ PDF Chat	Germs of singular Levi-flat hypersurfaces and holomorphic foliations	2015	Rasul Shafikov Alexandre Sukhov
+	On singular real analytic Levi-flat foliations	2018	Arturo Fernández‐Pérez Rogério Mol Rudy Rosas
+ PDF Chat	On singular real analytic Levi-flat foliations	2020	Arturo Fernández‐Pérez Rogério Mol Rudy Rosas
+	On singular real analytic Levi-flat foliations	2018	Arturo Fernández-Pérez Rogério Mol Rudy Rosas
+	Chow's theorem for real analytic Levi-flat hypersurfaces	2021	Arturo Fernández-Pérez Rogério Mol Rudy Rosas
+ PDF Chat	A note on projective Levi flats and minimal sets of algebraic foliations	1999	Alcides Lins Neto
+ PDF Chat	On Levi flat hypersurfaces with transversely affine foliation	2022	Masanori Adachi Séverine Biard
+ PDF Chat	Holomorphic Continuation of Smooth Functions Over Levi-Flat Hypersurfaces	1977	Eric Bedford
+ PDF Chat	Chow's theorem for real analytic Levi-flat hypersurfaces	2022	Arturo Fernández‐Pérez Rogério Mol Rudy Rosas
+	On Levi-Flat Hypersurfaces with Generic Real Singular Set	2012	Arturo Fernández‐Pérez
+ PDF Chat	Local Normal Forms of Singular Levi-Flat Hypersurfaces	2018	Arturo Fernández‐Pérez Gustavo Marra

Works That Cite This (24)

Action	Title	Year	Authors
+ PDF Chat	Dicritical singularities and laminar currents on Levi-flat hypersurfaces	2017	Sergey Pinchuk Rasul Shafikov Alexandre Borisovich Sukhov
+ PDF Chat	Holomorphic Foliations Tangent to Levi-Flat Subsets	2018	Jane Bretas Arturo Fernández‐Pérez Rogério Mol
+	Pull-back of singular Levi-flat hypersurfaces	2021	Andrés Beltrán Arturo Fernández‐Pérez Hernán Neciosup
+	On Levi-Flat Hypersurfaces with Generic Real Singular Set	2012	Arturo Fernández‐Pérez
+	Lehmann-Suwa residues of codimension one holomorphic foliations and applications	2018	Arturo Fernández‐Pérez Jimmy Támara
+	Holomorphic foliations tangent to Levi-flat subsets	2017	Jane Bretas Arturo Fernández‐Pérez Rogério Mol
+ PDF Chat	Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations	2017	Andrés Beltrán Arturo Fernández‐Pérez Hernán Neciosup
+	Levi-Flat Hypersurfaces Tangent to Projective Foliations	2013	Arturo Fernández‐Pérez
+ PDF Chat	On Levi-flat hypersurfaces tangent to holomorphic webs	2011	Arturo Fernández‐Pérez
+	On the dynamics of foliations in $\mathbb{P}^n$ tangent to Levi-flat hypersurfaces	2014	Arturo Fernández‐Pérez Rogério Mol Rudy Rosas

Works Cited by This (5)

Action	Title	Year	Authors
+	Introduction to Complex Analytic Geometry	1991	Stanisław Łojasiewicz
+	Singular Levi-flat real analytic hypersurfaces	1999	D. Burns Xianghong Gong
+	Real Submanifolds in Complex Space and Their Mappings	1998	Baouendi M. Salah Rothschild Linda Preiss Peter Ebenfelt
+ PDF Chat	Reduction of the singularities of codimension one singular foliations in dimension three	2004	Felipe Cano
+	Pseudoconvex Domains with Real-Analytic Boundary	1978	Klas Diederich John Erik Fornæss