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Local Levi-flat hypersurfaces invariants by a codimension one holomorphic foliation

2011; Johns Hopkins University Press; Volume: 133; Issue: 3 Linguagem: Inglês

10.1353/ajm.2011.0018

1080-6377

Dominique Cerveau, Alcides Lins Neto,

Advanced Differential Equations and Dynamical Systems

In this paper we study codimension one holomorphic foliations leaving invariant real analytic hypersurfaces. In particular, we prove that a germ of real analytic Levi-flat hypersurface with sufficiently ``small" singular set is given by the zeroes of the imaginary part of a holomorphic function.