| dc.contributor.author |
Thai, Do Duc |
| dc.contributor.author |
Thai, Do Duc |
| dc.contributor.author |
Thomas, Pascal J. |
| dc.contributor.author |
Thomas, Pascal J. |
| dc.date |
2001 |
| dc.identifier |
https://ddd.uab.cat/record/1969 |
| dc.identifier |
urn:10.5565/PUBLMAT_45201_07 |
| dc.identifier |
urn:10.5565/PUBLMAT_45201_07 |
| dc.identifier |
urn:oai:ddd.uab.cat:1969 |
| dc.identifier |
urn:oai:ddd.uab.cat:1969 |
| dc.identifier |
urn:articleid:20144350v45n2p421 |
| dc.identifier |
urn:articleid:20144350v45n2p421 |
| dc.identifier |
urn:oai:raco.cat:article/38024 |
| dc.identifier |
urn:oai:raco.cat:article/38024 |
| dc.identifier |
urn:wos_id:000173200500007 |
| dc.identifier |
urn:wos_id:000173200500007 |
| dc.format |
application/pdf |
| dc.language |
eng |
| dc.publisher |
|
| dc.relation |
Publicacions matemàtiques ; V. 45 N. 2 (2001), p. 421-429 |
| dc.rights |
open access |
| dc.rights |
Tots els drets reservats. |
| dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
| dc.title |
On D*-extension property of the Hartogs domains |
| dc.type |
Article |
| dc.description.abstract |
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. |
| dc.description.abstract |
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. |
