Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
type: Item
instance of: scholarly article
title: Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
zbMATH Open document ID: 1028.32008
author: Bo Berndtsson
author: Jean-Pierre Rosay
publication date: 2003-06-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/116057
review text: Two holomorphic vector bundles \(E\), \(F\) on a complex manifold are said to be quasi-isometric if there is a bundle map \(f: E \rightarrow F\) and a constant \(c>0\) such that \(1/c\|v\|_E \leq \|f(v)\|_F \leq c\|v\|_E\) for every \(v\in E\). Here the authors give a sufficient condition for a bundle \(E\) on the unit disk of \(\mathbb{C}\) to be quasi-isometric to the trivial bundle. They use their method of proof to obtain a version of Cartan's lemma on the factorization of holomorphic matrices with uniform bounds for the solution.
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 30G20
zbMATH DE Number: 1940716
zbMATH Keywords: holomorphic vector bundle
zbMATH Keywords: Hermitian vector bundle
zbMATH Keywords: Hermitian holomorphic vector bundle
zbMATH Keywords: maximum principle
reviewed by: E. Ballico
MaRDI profile type: Publication
OpenAlex ID: W2465141990
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DOI: 10.5802/AIF.1964
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1940716