报告题目：Fully nonlinear equations on manifolds and related geometric problems
报 告 人：关波（俄亥俄州立大学 教授）
会议时间：2023年11月20日10:00开始
会议地点：9号楼 113报告厅
报告摘要：In this talk we discuss fully nonlinear PDEs on real or complex manifolds and their connections to geometric problems. We shall start with some interesting PDE proofs of important inequalities in geometry and analysis. We then move on to consider a general class of fully nonlinear equations which cover most of equations arising from geometric problems. In the second part we report progresses over the last ten years in the effort to solving these equations on manifolds, both for the Dirichlet problem and equations on closed manifolds. At the end we introduce some new equations for differential forms of higher rank, more specifically real (p, p) forms for p > 1 on complex manifolds, which were motivated by the important roles of such forms in complex and algebraic geometry. The talk is based on joint work with my student Mathew George and other collaborators.
报告人简介：关波，美国俄亥俄州立大学数学教授。研究方向为非线性偏微分方程和几何分析，主要研究工作包括一般区域/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；以及实或复流形上一般完全非线性偏微分方程。其学术论文发表在Adv. Math., Amer. J. Math., Annals of Math., CPAM, Duke Math. J., JDG, J. Eur. Math. Soc., J. Reine Angew. Math.等数学期刊上。
