Let $M^n$ be a complete noncompact K\"ahler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that $M$ is biholomorphic to $\mathbb{C}^n$.
This confirms the uniformization conjecture of Yau under the assumption $M$ has maximal volume growth.
@inproceedings{ganggromov-hausdorff,
title={Gromov-Hausdorff limits of Kahler manifolds with bisectional curvature lower bound II},
author={Gang Liu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170409204847221109739},
}
Gang Liu. Gromov-Hausdorff limits of Kahler manifolds with bisectional curvature lower bound II. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170409204847221109739.