走向现代数学学术报告 - 钟春平教授（No. 822)

报告题目：Characterization of holomorphic invariant Kähler-Finsler metrics on the unit polydisk and the classical domains

报告时间：2025年10月24日 10:00

腾讯会议ID：906-823-371

报 告 人：钟春平 教授（厦门大学）

邀 请 人：朱剑峰 教授

报告摘要：In this talk we show that there exists no holomorphic invariant complex Finsler metric other than a positive constant multiple of the Bergman metric on the open unit ball in C^n, while there exist infinitely many holomorphic invariant Kähler-Finsler metrics on the unit polydisk in C^n, which are non-Hermitian quadratic. This phenomenon also happens on the irreducible bounded symmetric domains of type I-IV, namely the classical domains. We obtain characterizations of holomorphic invariant metrics both on the unit polydisk and the classical domains. We also obtain the corresponding Schwarz lemmas on the unit polydisk and the classical domains whenever they are endowed with arbitrary holomorphic invariant Kähler-Finsler metrics, respectively. Our results show that the Lu constant associated to these homogeneous Kähler-Finsler manifolds is both an analytic invariant and a geometric invariant which can be better understood in complex Finsler setting.

报告人简介：钟春平，厦门大学数学科学学院教授、博士生导师。从事多复变与复芬斯勒几何研究。在Math. Ann., J. Geom. Anal., Ann. Mat. Pura Appl., Sci. China Math. 等国际知名期刊发表60余篇学术论文。主持国家自然科学基金7项。2013年获得福建省自然科学基金杰青资助.