主持人：刘钢
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 0 < Θ < π/2 (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.
报告人简介：
邱国寰，现任中国科做爱视频数学与系统科学研究院副研究员。2016年获得中国科学技术大学博士学位，随后在加拿大麦吉尔大学从事博士后研究，并于香港中文大学任研究助理教授。2021年起就职于中国科做爱视频数学与系统科学研究院。他曾荣获中国数学会钟家庆奖，并入选国家海外青年人才计划。他的研究聚焦于椭圆型偏微分方程与几何分析。其代表性工作包括：解决N.Trudinger纽曼问题猜想；证明三维正数量曲率方程的内部估计，以及高维2-Hessian方程凸解的二阶导数内估计；建立空间形式中的Reilly型积分公式等。其相关成果多次发表在 Amer. J. Math.、Comm. Math. Phys.、Duke Math. J.、IMRN等国际权威期刊。
