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

2007/02/09 by Chau, Albert, Tam, Luen-Fai
#35K90 #53C55 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0702257

Abstract

Yau's uniformization conjecture states: a complete noncompact Kähler manifold with positive holomorphic bisectional curvature is biholomorphic to \ceⁿ. 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.

Related

• On Yau's uniformization conjecture
• A Uniformization Theorem Of Complete Noncompact Kähler Surfaces With Positive Bisectional Curvature
• Gradient Kähler-Ricci solitons and a uniformization conjecture
• Chern-Ricci flows on noncompact complex manifolds
• Ricci flow on compact Kähler manifolds of positive bisectional curvature