Fully nonlinear PDEs equations on manifolds and estimates under weaker conditions on symmetry and concavity
数学公众报告
报告题目(Title)：Fully nonlinear PDEs equations on manifolds and estimates under weaker conditions on symmetry and concavity
报告人(Speaker)：关波 教授（Ohio State University）
地点(Place)：后主楼1124
时间(Time)：2023年12月4日(周一)，16:00-17:00
邀请人(Inviter)：葛建全
报告摘要
We consider a general class of fully nonlinear equations which cover most of equations arising from geometric problems, and 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. In the talk we shall discuss the roles of symmetry and concavity in the study of fully nonlinear PDEs, and how these conditions can be weakened in deriving a priori estimates up to second order.
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 Annals of Math., CPAM, Duke Math. J., JDG, J. Eur. Math. Soc., J. Reine Angew. Math. Adv. Math., Amer. J. Math.,等国际一流期刊上。
