On D*-extension property of the Hartogs domains.

Thai, Do Duc, and Thomas, Pascal J.. "On D*-extension property of the Hartogs domains.." Publicacions Matemàtiques 45.2 (2001): 421-429. <http://eudml.org/doc/41436>.

@article{Thai2001,
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 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.},
author = {Thai, Do Duc, Thomas, Pascal J.},
journal = {Publicacions Matemàtiques},
keywords = {Funciones holomorfas de varias variables; Espacio hiperbólico; Dominios pseudoconvexos; Singularidades; Kobayashi hyperbolicity; removable singularities; Kontinuitätssatz; extension through pluripolar sets; -extension property; Hartogs domain},
language = {eng},
number = {2},
pages = {421-429},
title = {On D*-extension property of the Hartogs domains.},
url = {http://eudml.org/doc/41436},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Thai, Do Duc
AU - Thomas, Pascal J.
TI - On D*-extension property of the Hartogs domains.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 2
SP - 421
EP - 429
AB - 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.
LA - eng
KW - Funciones holomorfas de varias variables; Espacio hiperbólico; Dominios pseudoconvexos; Singularidades; Kobayashi hyperbolicity; removable singularities; Kontinuitätssatz; extension through pluripolar sets; -extension property; Hartogs domain
UR - http://eudml.org/doc/41436
ER -