Invariant metrics on negatively pinched complete Kahler manifolds
Student No.:100
Time:Tuesday 10:00-11:00, 2017.12.5
Instructor:Shing-Tung Yau  [Tsinghua University, Harvard University]
Place:Lecture Hall, 3rd floor, Jin Chun Yuan West Bldg.
Starting Date:2017-11-24
Ending Date:2017-12-6

Abstract: We prove that a complete Kahler manifold with holomorphic curvature bounded between two negative constants admits a unique complete Kahler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly equivalent to the background Kahler metric. Furthermore, all three metrics are shown to be uniformly equivalent to the Bergman metric, if the complete Kahler manifold is simply-connected, with the sectional curvature bounded between two negative constants. In particular, we confirm two conjectures of R. E. Greene and H. Wu posted in 1979.