题目：A Priori Interior Estimates for Special Lagrangian Curvature Equations

报告人：邱国寰 教授 (中科院数学与系统科学研究院)

地点：致远楼101室

时间：2025年1月3日 10:00-11:00

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 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.

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