[콜로퀴엄] Uniformization theorems associated to Bergman metric and some open problems (23/10/6)

1. 일 시 : 2023년 10월 06일 (금요일) 오후 4시 

2. 장 소 : 아산이학관 526호 (권택연 세미나실)

3. 연 사 : Song-Ying Li (University of California, Irvine) 

4. 제 목 : Uniformization theorems associated to Bergman metric and some open problems

5. 요 약  In this talk, I will present a joint work with Xiaojun Huang (from Rutgers University). We study domains in Cn or Stein manifolds M such that their Bergman metrics have constant holomorphic sectional curvature κ. We prove a uniformization theorem when κ < 0 through the Calabi rigidity theorem and holomorphic extension theorems. We also discuss the case when κ ≥ 0. We provide several interesting examples of existence of such M. Under certain conditions on M, we prove that the Bergman metric of M can not have non-negative constant holomorphic sectional curvatures. I will also present several open problems related to Bergman metrics.