报告题目：A bridge connecting convex analysis and complex analysis, and the union problem for domains with partial pseudoconvex boundaries
时 间：2026年11月10日（星期二）10：00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）
参加对象：相关方向教师和研究生
报告摘要：We propose a way to connect complex analysis and convex analysis. As applications, we derive some results about L2-estimates for the d-equation and prove some curvature positivity on convex domains from the well-known L2-estimate for the dbar-equation or from results we have proved in complex analysis. On the other hand, we show that a smooth bounded domain in Cn admitting a partial pseudoconvex exhaustion remains partially pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-q-convex domains. Furthermore, we obtain several convex analogues in Rn. These results represent joint work with Fusheng Deng, Weiwen Jiang, Xiangsen Qin and Xujun Zhang.
报告人简介：胡金金，北京理工大学预聘助理教授，博士毕业于中国科学院大学数学科学学院，师从邓富声教授。胡金金的研究方向是多复变与复几何领域中的直接像丛的曲率正性以及dbar方程的最优L2理论等，研究结果发表在Math. Ann., J. Func. Anal.等国际顶尖数学期刊上。