Remarks on the Kobayashi hyperbolicity of complex spaces
type: Item
instance of: scholarly article
title: Remarks on the Kobayashi hyperbolicity of complex spaces
zbMATH Open document ID: 1201.32015
author: Nguyen Van Trao
author: Tran Hue Minh
published in: Acta Mathematica Vietnamica
publication date: 2010-09-07T00:00:00Z
full work available at URL: Toc ACTA 3 34.htm
review text: The hyperbolicity of Hartogs type domains has been studied for many years and many people obtained different results for some special cases. In the paper under review, the authors find the necessary and sufficient conditions for the hyperbolicity of Hartogs type domains in the general case and also find necessary and sufficient conditions for the tautness of the same domains. Furthermore, the authors generalize a result by \textit{Do Duc Thai, Pham Viet Duc}, and \textit{Tran Hue Minh} [Kyushu J. Math. 59, No.~2, 231--252 (2005; Zbl 1087.32011)], which is about hyperbolic imbeddedness. In the final part, the authors study the convergence of invariant functions and extend \textit{M. Kobayashi}'s result [Complex Variables, Theory Appl. 47, No.~2, 155--165 (2002; Zbl 1031.32015)] to some other cases.
reviewed by: Joonhyung Kim
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 32U35
zbMATH DE Number: 5780194
zbMATH Keywords: Hartogs type domains
zbMATH Keywords: hyperbolicity
zbMATH Keywords: hyperbolic imbeddedness
zbMATH Keywords: pluricomplex Green functions
zbMATH Keywords: Lempert function
zbMATH Keywords: Carathéodory function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5780194