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In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete non-compact complex two dimensional Kähler manifold M of positive and bounded holomorphic bisectional curvature, suppose its geodesic balls have maximal volume growth, then M is biholomorphic to C2. This gives a partial affirmative answer to the well-known conjecture of Yau  on uniformization theorem. During the proof, we also verify an interesting gap phenomenon, predicted by Yau in , which says that a Kähler manifold as above automatically has quadratic curvature decay at infinity in the average sense.