报告学者：邱国寰

报告者单位：中科院数学所

报告时间：2025/04/11  3:00-4:00 pm

报告地点：七教7215

Abstract: 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 maybe a singular C^{1,a} solution in supercritical case which is different from the special Lagrangian equations. We have also demonstrated that these gradient  estimates of these curvature equations also 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.

报告学者简介：邱国寰，现任中国科学院数学与系统科学研究院副研究员。2009年毕业于西北大学，2016年于中科大获博士学位。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。2019年获得中国数学会钟家庆奖。主要研究方向为偏微分方程和几何分析。其研究成果接收和发表在Amer. J. Math，Comm. Math.Phys., Duke Math J., IMRN等国际一流数学学术期刊上。