Liouville-type theorems for foliations with complex leaves
[Théorèmes du type Liouville pour feuilletages avec feuilles complexes]
Della Sala, Giuseppe1
1 Institut fuer Mathematik Nordbergstrasse 15 1090 Wien (Autriche)
Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 711-725.

Dans cet article nous considérons différentes questions relatives à la structure du feuilletage de certaines sous-variétés S⊂ℂ n , en particulier les variétés Levi-plates. Comme schéma général, on suppose que S est bornée le long d’une coordonnée (ou d’un sous-ensemble des coordonnées), et on montre que les feuilles complexes de son feuilletage sont des plans.

In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds S of ℂ n , in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.

DOI : 10.5802/aif.2537
Classification : 32V40
Keywords: Levi flat submanifolds, Liouville theorem, analytic multifunctions
Mot clés : sous-variétés Levi-plates, Théorème de Liouville, multifonctions analytiques
Della Sala, Giuseppe 1

1 Institut fuer Mathematik Nordbergstrasse 15 1090 Wien (Autriche) 
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Della Sala, Giuseppe. Liouville-type theorems for foliations with complex leaves. Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 711-725. doi : 10.5802/aif.2537. http://www.numdam.org/articles/10.5802/aif.2537/

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