Resumen de Extension d'homéomorphismes CR entre variétés polynômialement rigides

Patrick Lahondès

• Let $f\colon M \rightarrow M'$ be a CR homeomorphism between two minimal, rigid polynomial varieties of $\mathbb{C}^n$ without holomorphic curves. We show that $f$ extends biholomorphically in a neighborhood of $M$ if $f$ extends holomorphically in a neighborghood of a point $p_0\in M$ or if $f$ is of class $\mathcal{C}^1$. In the other hand, in case $M$ and $M'$ are two algebraic hypersurfaces, we obtain the extension without supplementary conditions.