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.
@article{urn:eudml:doc:41436, title = {On D*-extension property of the Hartogs domains.}, journal = {Publicacions Matem\`atiques}, volume = {45}, year = {2001}, pages = {421-429}, mrnumber = {MR1876915}, zbl = {0994.32014}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41436} }
Thai, Do Duc; Thomas, Pascal J. On D*-extension property of the Hartogs domains.. Publicacions Matemàtiques, Tome 45 (2001) pp. 421-429. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41436/