A survey on the Kähler-Ricci flow and Yau's uniformization conjecture

Details A survey on the Kähler-Ricci flow and Yau's uniformization conjecture A survey on the Kähler-Ricci flow and Yau's uniformization conjecture

2007-02-09

arxiv.org/abs/math/0702257v2

Mathematics

Differential Geometry

Theorem 4.4 has been improved. Theorem 6.6 has been added

Scientific paper

Yau's uniformization conjecture states: a complete noncompact K\"ahler manifold with positive holomorphic bisectional curvature is biholomorphic to $\ce^n$. The K\"ahler-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 K\"ahler-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.

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