Distortion theorems for convex mappings on homogeneous balls
type: Item
instance of: scholarly article
title: Distortion theorems for convex mappings on homogeneous balls
zbMATH Open document ID: 1208.32015
author: G. Kohr
author: Cho-Ho Chu
author: H. Hamada
author: T. Honda
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-20T00:00:00Z
review text: The authors prove a distorsion theorem for normalized holomorphic convex maps defined on a homogeneous unit ball \(B\) of a complex Banach space~\(X\), where a holomorphic map \(f: B\to X\) is normalized if \(f(O)=O\) and \(df_O=\text{id}\), and it is convex if it is a biholomorphism and its image is convex. Under these hypotheses, the authors give lower and upper bounds both for the norm of the differential \(df\) and for the distance \(\|f(a)-f(b)\|\) between two points in the image, generalizing various finite-dimensional distorsion theorems.
reviewed by: Marco Abate
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5757888
zbMATH Keywords: convex holomorphic map
zbMATH Keywords: distorsion theorem
zbMATH Keywords: homogeneous ball
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.03.014
OpenAlex ID: W2072914417
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DOI: 10.1016/J.JMAA.2010.03.014
description: scientific article; zbMATH DE number 5757888