Extension d'homéomorphismes CR entre variétés polynômialement rigides

Autores: Patrick Lahondès
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 46, Nº 2, 2002, págs. 327-352
Idioma: francés
DOI: 10.5565/publmat_46202_02
Títulos paralelos:
- Extensión de homeomorfismos CR entre variedades polinomialmente rígidas
- Extension of CR homeomorphisms between rigid polynomial varieties
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Resumen
- 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.