Bloch principle and estimates of the Kobayashi metric of domains in \(\mathbb{C}^2\)
type: Item
instance of: scholarly article
title: Bloch principle and estimates of the Kobayashi metric of domains in \(\mathbb{C}^2\)
zbMATH Open document ID: 1040.32011
DOI: 10.1007/BF02930994
published in: The Journal of Geometric Analysis
publication date: 2003-12-04T00:00:00Z
review text: This paper studies the Bloch asymptotic principle for smooth pseudoconvex domains of finite type in \(\mathbb{C}^2\). Combining the renormalization method used by Gromov in the context of harmonic mappings with a technique of coordinate dilation, it gives a construction of a pseudo-metric equivalent to the Kobayashi metric of these domains, and further with this pseudo-metric constructs a sequence of holomorphic mappings from a domain in \(\mathbb{C}^k\) to a smooth pseudoconvex domain of finite type in \(\mathbb{C}^2\) whose limit is also holomorphic in a polynomially-rigid pseudoconvex domain. Here is provided a totally elementary proof for a result of \textit{D. W. Catlin} [Math. Z. 200, 429--466 (1989; Zbl 0661.32030)] which is quite useful in study of the immersions and rigidity of harmonic maps.
reviewed by: Na Jisheng
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32T25
zbMATH DE Number: 2013173
zbMATH Keywords: pseudoconvex domain of finite type
zbMATH Keywords: Kobayashi metric
zbMATH Keywords: holomorphic map
zbMATH Keywords: coordinate dilation
author: François Berteloot
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2013173