Yau's uniformization conjecture for complete noncompact Kähler manifolds

Let $M$ be a complete noncompact $m$-dimensional Kähler manifold with positive holomorphic bisectional curvature.

Yau's uniformization conjecture. If $M$ has these properties, then $M$ is biholomorphic to the standard $m$-dimensional complex Euclidean space

$$\mathbb{C}^{m}.$$

This is a classical uniformization problem in Kähler geometry. The source describes substantial progress under additional hypotheses, including maximal volume growth and curvature assumptions, but does not establish the conjecture in the stated generality.