no. 3
Quasi-isometric vector bundles and bounded factorization of holomorphic matrices
[Fibrés vectoriels quasi isométriques et factorisation bornée des matrices holomorphes]
Berndtsson, Bo1 ; Rosay, Jean-Pierre2
1 Chalmers University of Technology and the University of Göteborg, Department of Mathematics, 412 96 Göteborg (Suède)
2 University of Wisconsin, Department of Mathematics, Madison WI 53706 (USA)
Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 885-901.

Nous donnons une condition suffisante pour qu'un fibré vectoriel holomorphe hermitien sur le disque soit quasi isométrique au fibré trivial. Une des conséquences est une version du Lemme de Cartan sur la factorisation des matrices holomorphes pour les matrices holomorphes bornées.

We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.

DOI : 10.5802/aif.1964
Classification : 46F20, 32A26
Keywords: vector bundle, maximum principle
Mot clés : fibré vectoriel, principe du maximum
Berndtsson, Bo 1 ; Rosay, Jean-Pierre 2

1 Chalmers University of Technology and the University of Göteborg, Department of Mathematics, 412 96 Göteborg (Suède)
2 University of Wisconsin, Department of Mathematics, Madison WI 53706 (USA) 
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Berndtsson, Bo; Rosay, Jean-Pierre. Quasi-isometric vector bundles and bounded factorization of holomorphic matrices. Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 885-901. doi : 10.5802/aif.1964. http://www.numdam.org/articles/10.5802/aif.1964/

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