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Disques analytiques et problèmes au bord en géométries complexe et presque complexe

Abstract : This thesis deals with the study of analytic discs attached to some submanifold.

In the first part, we obtain an explicit parametrization of some special family of analytic discs attached to different types of non-degenerate real hypersurfaces in $\C^n$. These discs are invariant under the action of biholomorphisms. We use this parametrization to construct a circular representation of the hypersurface, and we also get some properties of uniqueness for biholomorphisms.

In the second part of this thesis, we consider proper pseudo-holomorphic maps between two strictly pseudoconvex bounded domains in almost complex manifolds. We prove that such a map extends up to the boundary. We establish the link between the regularity of the extension and the regularity of the amost complex structures, and we give explicit estimates for the Hölderian norms.
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Contributor : Léa Blanc-Centi <>
Submitted on : Tuesday, April 3, 2007 - 1:32:43 PM
Last modification on : Wednesday, October 10, 2018 - 1:26:27 AM
Long-term archiving on: : Friday, September 21, 2012 - 1:42:44 PM


  • HAL Id : tel-00139726, version 1



Léa Blanc-Centi. Disques analytiques et problèmes au bord en géométries complexe et presque complexe. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2006. Français. ⟨tel-00139726⟩



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