On the complex structure of K\"ahler manifolds with nonnegative curvature

We study the asymptotic behavior of the K"ahler-Ricci flow on K"ahler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact K"ahler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space ${\text{C}}^n$. We also show that the volume growth condition can be removed if we assume $(M,g)$ has average quadratic scalar curvature decay (see Theorem 2.1) and positive curvature operator.