Surveys in Differential Geometry
Volume 12 (2007)
A survey of the Kähler-Ricci Flow and Yau’s Uniformization Conjecture
Pages: 21 – 46
Yau’s uniformization conjecture states: a complete noncompact Kähler manifold with positive holomorphic bisectional curvature is biholomorphic to Cn. The Kähler-Ricci flow has provided a powerful tool in understanding the conjecture, and has been used to verify the conjecture in several important cases. In this article we present a survey of the Kähler-Ricci flow with focus on its application to uniformization. Other interesting methods and results related to the study of Yau’s conjecture are also discussed.