Surveys in Differential Geometry

Volume 12 (2007)

A survey of the Kähler-Ricci Flow and Yau’s Uniformization Conjecture

Pages: 21 – 46



A. Chau (Waterloo University, Department of Mathematics, The University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada.)

L.-F. Tam (Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China.)


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.

Full Text (PDF format)