应兰州大学数学与统计学院邀请,中国科学院数学与系统科学研究院邱国寰副研究员将于2025年9月17日上午作线上学术报告，欢迎全校师生参加.

报告题目：A priori interior estimates for special Lagrangian curvature equations

时 间：2025年9月17日(星期三)9:00

地 点：腾讯会议（会议号：910-508-995）

报告摘要：We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex cases. The supercritical case, however, is distinct from the special Lagrangian equations. In dimension two, we observe that this curvature equation is equivalent to the equation arising in the optimal transportation problem with a‘relative heat’cost function, as discussed in Brenier's paper.

When(supercritical phase), the equation violates the Ma-Trudinger-Wang condition. However, Loeper's counterexample for general optimal transport problems does not directly apply here, as this concerns a specific optimal transport problem with fixed density functions. Moreover, the interior gradient estimates for this curvature equation are simpler than those for the special Lagrangian equations. We have demonstrated that these gradient estimates also hold for subcritical phases. It is worth noting that for the special Lagrangian equation, particularly in subcritical phases, the interior gradient estimate remains an open problem. This is joint work with Xingchen Zhou.

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报告人简介

邱国寰(Guohuan Qiu),现任中国科学院数学与系统科学研究院副研究员,2016年于中国科学技术大学获博士学位.先后在麦吉尔大学做博士后和香港中文大学任研究助理教授.2021年入职中科院数学所，现任中国科学院数学与系统科学研究院副研究员.曾获得中国数学会钟家庆奖以及入选国家海外青年人才计划.主要研究方向为椭圆方程和几何分析,和合作者解决了海森方程的纽曼边界问题;和合作者解决了高维2-海森方程凸解的二阶导数内估计问题;和合作者得到了空间形式的Reilly积分公式;解决了三维超曲面数量曲率方程内估计问题.结果发表于Duke Math J., Comm. Math. Phys., IMRN等国际著名学术期刊。

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