# Extending holomorphic mappings from subvarieties in Stein manifolds

• [1] Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia)
• Volume: 55, Issue: 3, page 733-751
• ISSN: 0373-0956

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## Abstract

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Suppose that $Y$ is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space ${ℂ}^{n}$ to $Y$ is a uniform limit of entire maps ${ℂ}^{n}\to Y$. We prove that a holomorphic map ${X}_{0}\to Y$ from a closed complex subvariety ${X}_{0}$ in a Stein manifold $X$ admits a holomorphic extension $X\to Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

## How to cite

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Forstneric, Franc. "Extending holomorphic mappings from subvarieties in Stein manifolds." Annales de l’institut Fourier 55.3 (2005): 733-751. <http://eudml.org/doc/116206>.

@article{Forstneric2005,
abstract = {Suppose that $Y$ is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space $\{\mathbb \{C\}\}^n$ to $Y$ is a uniform limit of entire maps $\{\mathbb \{C\}\}^n\rightarrow Y$. We prove that a holomorphic map $X_0 \rightarrow Y$ from a closed complex subvariety $X_0$ in a Stein manifold $X$ admits a holomorphic extension $X\rightarrow Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.},
affiliation = {Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia)},
author = {Forstneric, Franc},
journal = {Annales de l’institut Fourier},
keywords = {Stein manifold; holomorphic mappings; Oka property; holomorphic map; convex approximation property},
language = {eng},
number = {3},
pages = {733-751},
publisher = {Association des Annales de l'Institut Fourier},
title = {Extending holomorphic mappings from subvarieties in Stein manifolds},
url = {http://eudml.org/doc/116206},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Forstneric, Franc
TI - Extending holomorphic mappings from subvarieties in Stein manifolds
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 3
SP - 733
EP - 751
AB - Suppose that $Y$ is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space ${\mathbb {C}}^n$ to $Y$ is a uniform limit of entire maps ${\mathbb {C}}^n\rightarrow Y$. We prove that a holomorphic map $X_0 \rightarrow Y$ from a closed complex subvariety $X_0$ in a Stein manifold $X$ admits a holomorphic extension $X\rightarrow Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.
LA - eng
KW - Stein manifold; holomorphic mappings; Oka property; holomorphic map; convex approximation property
UR - http://eudml.org/doc/116206
ER -

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