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Fall 2003 Some remarks about Reinhardt domains in $\mathbf{C}^n$
Nguyen Quang Dieu, Le Mau Hai
Illinois J. Math. 47(3): 699-708 (Fall 2003). DOI: 10.1215/ijm/1258138188

Abstract

We show that, given a bounded Reinhardt domain $D$ in $\mathbb{C}^n$, there exists a hyperconvex domain $\Omega$ such that $\Omega$ contains $D$ and every holomorphic function on a neighborhood of $\overline{D}$ extends to a neighborhood of $\overline{\Omega}$. As a consequence of this result, we recover an earlier result stating that every bounded fat Reinhardt domain having a Stein neighbourhoods basis must be hyperconvex. We also study the connection between the Caratheodory hyperbolicity of a Reinhardt domain and that of its envelope of holomorphy. We give an example of a Caratheodory hyperbolic Reinhardt domain in $\mathbf{C}^3$, for which the envelope of holomorphy is not Caratheodory hyperbolic, and we show that no such example exists in $\mathbf{C}^2$.

Citation

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Nguyen Quang Dieu. Le Mau Hai. "Some remarks about Reinhardt domains in $\mathbf{C}^n$." Illinois J. Math. 47 (3) 699 - 708, Fall 2003. https://doi.org/10.1215/ijm/1258138188

Information

Published: Fall 2003
First available in Project Euclid: 13 November 2009

zbMATH: 1033.32007
MathSciNet: MR2007231
Digital Object Identifier: 10.1215/ijm/1258138188

Subjects:
Primary: 32A07
Secondary: 32D15, 32Q45

Rights: Copyright © 2003 University of Illinois at Urbana-Champaign

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Vol.47 • No. 3 • Fall 2003
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