Presentación | Participantes | Bibliografía (DML-E) | Bibliografía adicional | Enlaces de interés | Otros proyectos DML | Ayuda
INICIO |
27 de julio de 2024
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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