# Ensembles localement pics dans les bords faiblement pseudoconvexes de $\C^n$.

Abstract : We give some sufficient conditions for a $C^{\omega}$ (resp. $C^{\infty}$)-totally real, complex-tangential, (n-1)-dimensional submanifold in a weakly pseudoconvex boundary of class $C^{\omega}$ (resp. $C^{\infty}$) to be a local peak set for the class $\mathcal{O}$ (resp. $A^{\infty}$). Next we give some results about interpolation submanifolds for the class $A^{\infty}$. In the case of the class $\mathcal{O}$ we have generalized the work of Boutet de Monvel and Iordan concerning the caracterization of peak curves in weakly pseudoconvex boundaries in $\C^2$. We have extended our results obtained for the class $\mathcal{O}$ to the class $A^{\infty}$ by using the methods of Hakim and Sibony which they have developed for strongly pseudoconvex boundaries. Finally we give consequencesof our sufficient conditions on Catlin's multitype.
The main difficulty of our work is that complex geometry in heigher dimensions has a nonisotropic structure. The caracteristic numbers of this anisotropy result in a delicate computation on weighted polynomials. It also turns out that these numbers are linked to Catlin's multitype for the points on the submanifold.
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Cited literature [20 references]

https://tel.archives-ouvertes.fr/tel-00084010
Contributor : Borhen Halouani <>
Submitted on : Wednesday, July 5, 2006 - 12:40:23 PM
Last modification on : Tuesday, January 5, 2021 - 5:24:02 PM
Long-term archiving on: : Monday, April 5, 2010 - 11:48:57 PM

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• HAL Id : tel-00084010, version 1

### Citation

Borhen Halouani. Ensembles localement pics dans les bords faiblement pseudoconvexes de $\C^n$.. Mathématiques [math]. Université du Littoral Côte d'Opale, 2006. Français. ⟨tel-00084010⟩

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