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On D*-extension property of the Hartogs domains
Thai, Do Duc
Thomas, Pascal J.

Data: 2001
Resum: 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 × C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by [phi] 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 [phi] is plurisubharmonic. We prove that H has the D*-extension property if and only if (i) X itself has the D*-extension property, (ii) [phi] takes only finite values and (iii) [phi] 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions matematiques, V. 45 N. 2 (2001) , p. 421-429, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_45201_07

9 p, 139.2 KB

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