91自拍

荔园学者Colloquium第一百五十九期

讲座题目：Bergman metrics have constant holomorphic sectional curvatures

主讲人：李松鹰 教授（美国加州大学尔湾分校）

讲座时间：2026年1月7日 16：00-17：00

讲座地点：91自拍 粤海校区汇星楼一号教室

内容摘要：I will talk about joint works 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. A well-known theorem of Lu Qi-Keng states that any bounded domains Ω in C n whose Bergman metric is complete and has a negative constant holomorphic sectional curvature if and only if it is biholomorphic to the unit ball Bn in C n . In practices, there are many domains whose Bergman metric are not complete but have constant holomorphic sectional curvatures. Recently, we generalize Lu’s theorem to unbounded domain whose Bergman metric may not be complete and prove the following theorem: Any Stein manifold of complex dimension n whose Bergman metric has non-positive holomorphic sectional curvatures if and only if it is biholomorphic to the unit ball in C n possible less a relatively closed pluripolor set. In the earlier paper, discussed Stein manifolds having positive constant holomorphic sectional curvature κ > 0. We first construct an interesting example of domain Ω ⊂ C2 so that its Bergman metric has holomorphic sectional curvature 2. Second, we prove that any complex manifold M of dimension n is Bergman separable and has positive constant holomorphic sectional curvature is biholomorphic to a domain in Pn with finite dimensional Bergman space A2 (M).

主讲人简介：李松鹰（Song-Ying Li)，美国加州大学尔湾分校 (UC, Irvine) 教授，多复变函数论国际著名专家，研究领域涵盖多复变函数论、非线性偏微分方程和调和分析。在Amer. J. Math., Adv. Math., J. Funct. Anal., J. London Math. Soc., J. Differ. Geom., Math. Ann.等国际知名期刊发表90余篇学术论文。

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