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.
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.
@article{AIF_2003__53_3_885_0, author = {Berndtsson, Bo and Rosay, Jean-Pierre}, title = {Quasi-isometric vector bundles and bounded factorization of holomorphic matrices}, journal = {Annales de l'Institut Fourier}, pages = {885--901}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {3}, year = {2003}, doi = {10.5802/aif.1964}, zbl = {1028.32008}, mrnumber = {2008445}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1964/} }
TY - JOUR TI - Quasi-isometric vector bundles and bounded factorization of holomorphic matrices JO - Annales de l'Institut Fourier PY - 2003 DA - 2003/// SP - 885 EP - 901 VL - 53 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1964/ UR - https://zbmath.org/?q=an%3A1028.32008 UR - https://www.ams.org/mathscinet-getitem?mr=2008445 UR - https://doi.org/10.5802/aif.1964 DO - 10.5802/aif.1964 LA - en ID - AIF_2003__53_3_885_0 ER -
%0 Journal Article %T Quasi-isometric vector bundles and bounded factorization of holomorphic matrices %J Annales de l'Institut Fourier %D 2003 %P 885-901 %V 53 %N 3 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.1964 %R 10.5802/aif.1964 %G en %F AIF_2003__53_3_885_0
Berndtsson, Bo; Rosay, Jean-Pierre. Quasi-isometric vector bundles and bounded factorization of holomorphic matrices. Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 885-901. doi : 10.5802/aif.1964. https://aif.centre-mersenne.org/articles/10.5802/aif.1964/
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