报告人：邱国寰博士后

         McGill大学

报告题目：Interior Hessian estimates for sigma-2 equations in dimension three

报告时间：2018年01月09日下午14:30

报告地点：海韵数理楼661

摘要：The interior regularity for solutions of the sigma_2 Hessian equation is a longstanding problem.Heinz first derived this interior estimate in dimension two. For higher dimensional Monge-Ampere equations, Pogorelov constructed his famous counter-examples even for f constant and convex solutions. Caffarelli-Nirenberg-Spruck studied more general fully nonlinear equations such as \sigma_{k} equations in their seminal work. And Urbas also constructed counter-examples with k greater than 3. The only unknown case is k=2. A major breakthrough was made by Warren-Yuan, they obtained a prior interior Hessian estimate for the equation \sigma_2=1 in dimension three.In this talk, I will present my recent work on how to deal this problem for a more general case in dimension three.

报告人简介：邱国寰，2016年中国科学技术大学获博士学位，现于加拿大McGill大学从事博士后研究。邱国寰博士在其博士论文中解决了Trudinger关于Hessian方程的Neumann问题的可解性的猜想。最近，他在2-Hessian方程上取得另一重大突破，证明了3维空间中的一般2-Hessian方程的内二阶估计以及3维流形中数量曲率方程的内曲率估计。

欢迎广大师生参加！