Quasi-isometric vector bundles and bounded factorization of holomorphic matrices (Q1395364)

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.