On D*-extension property of the Hartogs domains.

Título inglés On D*-extension property of the Hartogs domains.
Título español Sobre la propiedad D*-extensión de los dominios de Hartogs.
Autor/es Thai, Do Duc ; Thomas, Pascal J.
Organización Dep. Math. Inst. Pedagog., Hanoi, Vietnam;Lab. Math. "Émile Picard" Univ. Paul Sabatier, Toulouse, Francia
Revista 0214-1493
Publicación 2001, 45 (2): 421-429, 14 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex, H is pseudoconvex if and only if φ is plurisubharmonic.
We prove that H has the D*-extension property if and only if (i) X itself has the D*-extension property, (ii) φ takes only finite values and (iii) φ is plurisubharmonic. This implies the existence of domains which have the D*-extension property without being (Kobayashi) hyperbolic, and simplifies and generalizes the authors' previous such example.
Clasificación UNESCO 120211
Palabras clave español Funciones holomorfas de varias variables ; Espacio hiperbólico ; Dominios pseudoconvexos ; Singularidades
Código MathReviews MR1876915
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