Comptes Rendus
no. 2
Complex Analysis
CR foliations, the strip-problem and Globevnik–Stout conjecture
[Des foliations CR, le problème ‘strip’ et la conjecture de Globevnik–Stout]

Présenté par : Pierre Lelong

Mark Agranovsky1
1 Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, 52900, Israel
Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 91-94.

On caractérise les fonctions CR sur les domains dans le plan et sur les hypersurfaces dans C2 en termes de leur eteindabilité aux discs analytiques attachés. Ça résulte de l'étude de la propagation, du bord à l'intérieur, de la dégénérescence des foliations CR des variétés de type tore solide. En particulier, pour les fonctions lisses on donne la réponse à deux questions ouvertes mentionnées dans le titre : sur la caractérisation des fonctions analytiques dans le plan complexe et sur la caractérisation des valeurs à bord des fonctions holomorphes dans un domain borné.

We characterize CR functions on planar domains and real hypersurfaces in C2 in terms of analytic extendibility into attached analytic discs. It is done by studying propagation, from the boundary into interior, of degeneracy of CR foliations of solid torus-like manifolds. In particular, we answer, for smooth functions, two open questions mentioned in the title: about characterization of analytic functions in the complex plane and about characterization of boundary values of holomorphic functions in bounded domains in Cn.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.06.013
Mark Agranovsky 1

1 Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, 52900, Israel 
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Mark Agranovsky. CR foliations, the strip-problem and Globevnik–Stout conjecture. Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 91-94. doi : 10.1016/j.crma.2006.06.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.06.013/

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