Gradient K\"ahler-Ricci solitons and a uniformization conjecture
Abstract
In this article we study the limiting behavior of the K\"ahler Ricci flow on complete non-compact K\"ahler manifolds. We provide sufficient conditions under which a complete non-compact gradient K\"ahler-Ricci soliton is biholomorphic to n. We also discuss the uniformization conjecture by Yau Y for complete non-compact K\"ahler manifolds with positive holomorphic bisectional curvature.
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