走向现代数学学术报告 - 郭常予教授（No. 824)

报告题目：Improved geometric characterization of Gromov hyperbolicity

报告时间：2025年11月4日 15:00

腾讯会议ID：908-160-106

报 告 人：郭常予 教授（山东大学）

邀 请 人：朱剑峰 教授

报告摘要：In a seminal work [Asterisque 2001], Bonk-Heinonen-Koskela developed a rich uniformization theory in metric spaces that extends the classical uniformization theorem of Riemann. Then they conjectured that the Gromov hyperbolicity of an Euclidean domain is equivalent to a geometric ball separation property plus the Gehring-Hayman inequality. In [Invent. Math. 2003], Balogh and Buckley successfully verified this conjecture for bounded Euclidean domains and then they asked a foundamental open problem: whether ball separation property indeed implies the Gehring-Hayman inequality.

In this talk, we shall develop a new measure independent approach to solve this open problem. Our result also significantly improved the main result of Koskela et al. in [Ann. Sci. Ec. Norm. Super. 2014]. The talk is based on recent joint works with Prof. M. Huang and Prof. X. Wang.

报告人简介：郭常予，山东大学数学与交叉科学研究中心教授，博士生导师。2009年本科毕业于北京师范大学，2013年博士毕业于芬兰于韦斯屈莱大学，导师为著名数学家Pekka Koskela院士。主要研究方向为复分析拟共形映照理论及其在偏微分方程中的应用。解决了多位国家数学家大会报告人提出来的若干公开问题与猜测，相关论文发表在Peking Math. J., Sci. China Math.等国际知名期刊。