讲座题目：Fully nonlinear PDEs: some developments in recent years and a new class of equations from complex geometry

主讲人：关波 教授 美国俄亥俄州立大学

讲座时间：2023年7月31日下午16:00 -17:00

讲座地点：阜成路综合楼1116

主讲人简介：

关波，美国俄亥俄州立大学数学系教授。研究方向为非线性偏微分方程和几何分析, 主要工作包括一般区域/流形上实和复蒙日-安培方程；常高斯曲率曲面的普拉图问题；闵可夫斯基问题的推广；关于双曲空间中具有常曲率和给定渐近边界的完备曲面的研究；以及实或复流形上一般完全非线性偏微分方程。其代表作发表在 Adv. Math., Amer. J. Math., Annals of Math., CPAM, Duke Math. J., JDG, J. Eur. Math. Soc., J. Reine Angew. Math.等国际一流期刊上。

主讲内容：

Fully nonlinear elliptic and parabolic equations play central roles in complex geometry, going back to the classical Calabi-Yau theorem. In recently years there have been increasing interests in such equations from geometric problems. In this talk we shall give a brief survey on recent developments, including work on equations on Riemannian manifolds, and discuss a new class of equations which fall outside the general framework established by Caffarelli-Nirenberg-Spruck. Part of this talk is based on joint work with my student Mathew George.