主持人：张德凯

报告人简介：
邱国寰，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。研究方向为：几何分析与偏微分方程。

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. 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 0 < Θ < π/2 (supercritical phase), the equation violates the Ma-Trudinger-Wang condition. So there may be a singular C^{1,a} solution in supercritical case which is different from the special Lagrangian equation. We have also demonstrated that these gradient estimates of these curvature equations hold for all constant 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.