# On D*-extension property of the Hartogs domains.

Publicacions Matemàtiques (2001)

- Volume: 45, Issue: 2, page 421-429
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topThai, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.