arXiv subjects

Marianne Peyron

Publications and source records attributed to Marianne Peyron.

2 recordsLinked to original sources

arXiv2013

Analyticité des applications CR dans des variétés presque complexes

We study the real analyticity of a CR mapping on the hypersurface $\h$ defined by $\h=\{z\in\C^n,\Re(z_n)+|z'|^2=0\}$ in model almost complex manifolds. We make use of a method of prolongation for the tangential Cauchy-Riemann equations and a result about complete systems. We also prove that a CR mapping is real analytic when the almost complex structure of the codomain is a deformation of a model structure and the function defining the hypersurface in the codomain has a particular form.

math.CV↗

arXiv2012

Théorème de Poincaré-Alexander pour les domaines modèles. Poincare-Alexander Theorem for model domains

The Poincaré-Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of $C^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly pseudoconvex homogeneous domain is biholomorphic to the unit ball. In an almost complex manifold, the unit ball is not the only strongly pseudoconvex homogeneous domain. A strongly pseudoconvex homogeneous domain is biholomorphic to a model domain. The aim of this paper is to extend this theorem to model domains.

math.CV↗